02-18-2016, 07:25 AM

Forums / Week 4 Forum / Topic 1: If Only I Had a System ...

Topic 1: If Only I Had a System ...

This will be your opportunity to be the teacher. Click on "View Full Description and attachments" below for the directions and questions. Be sure to open the file that says "MATH110 Read This First" before you jump in!

Read the attached files. First read the one entitled "MATH110 Read this first," and then open the file called "Systems of Equations Problems with Answers."

Pick ONE of the problems that has not already been solved, and demonstrate its solution using either the substitution or elimination method.

Click Start a New Conversation and make the problem number and topic (#10 Jarod and the Bunnies) the subject of your post.

The answers are at the end of the file, so don't just give an answer—we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!

This is a moderated forum. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order to get credit.

I will indicate in the grading comments if corrections need to be made. If you haven't received credit, first double-check for my comments in the gradebook. If everything looks OK, then Message me asking me to check on it.

You must make the necessary corrections and have your work posted in order to receive credit.

Your initial post is worth 10 points. It is not necessary to respond to 2 classmates on this forum, although a request for clarification on the procedure used would be appropriate. Also, I'm sure that a "Thank You" for an exceptionally clear explanation would be welcome!

Please sign ALL your Forum posts with the name that you like to be called - it makes it so much easier for the rest of us to address you by your preferred name when we respond.

Questions:

Systems of Equations

1) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot

dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot

dogs and 4 bags of potato chips for $9.25. Find the cost of each item.

2) University Theater sold 556 tickets for a play. Tickets cost $22 per adult

and $12 per senior citizen. If total receipts were $8492, how many senior

citizen tickets were sold?

3) A tour group split into two groups when waiting in line for food at a fast

food counter. The first group bought 8 slices of pizza and 4 soft drinks

for $36.12. The second group bought 6 slices of pizza and 6 soft drinks

for $31.74. How much does one slice of pizza cost?

4) Tina Thompson scored 34 points in a recent basketball game without

making any 3-point shots. She scored 23 times, making several free

throws worth 1 point each and several field goals worth two points each.

How many free throws did she make? How many 2-point field goals did

she make?

5) Julio has found that his new car gets 36 miles per gallon on the highway

and 31 miles per gallon in the city. He recently drove 397 miles on 12

gallons of gasoline. How many miles did he drive on the highway? How

many miles did he drive in the city?

6) A textile company has specific dyeing and drying times for its different

cloths. A roll of Cloth A requires 65 minutes of dyeing time and 50

minutes of drying time. A roll of Cloth B requires 55 minutes of dyeing

time and 30 minutes of drying time. The production division allocates

2440 minutes of dyeing time and 1680 minutes of drying time for the

week. How many rolls of each cloth can be dyed and dried?

7) A bank teller has 54 $5 and $20 bills in her cash drawer. The value of the

bills is $780. How many $5 bills are there?

8) Jamil always throws loose change into a pencil holder on his desk and

takes it out every two weeks. This time it is all nickels and dimes. There

are 2 times as many dimes as nickels, and the value of the dimes is $1.65

more than the value of the nickels. How many nickels and dimes does

Jamil have?

9) A flat rectangular piece of aluminum has a perimeter of 60 inches. The

length is 14 inches longer than the width. Find the width.

10) Jarod is having a problem with rabbits getting into his vegetable garden,

so he decides to fence it in. The length of the garden is 8 feet more than 3

times the width. He needs 64 feet of fencing to do the job. Find the

length and width of the garden.

11) Two angles are supplementary if the sum of their measures is 180°. The

measure of the first angle is 18° less than two times the second angle.

Find the measure of each angle.

12) The three angles in a triangle always add up to 180°. If one angle in a

triangle is 72° and the second is 2 times the third, what are the three

angles?

13) An isosceles triangle is one in which two of the sides are congruent. The

perimeter of an isosceles triangle is 21 mm. If the length of the

congruent sides is 3 times the length of the third side, find the

dimensions of the triangle.

14) A chemist needs 130 milliliters of a 57% solution but has only 33% and

85% solutions available. Find how many milliliters of each that should be

mixed to get the desired solution.

15) Two lines that are not parallel are shown. Suppose that the measure of

angle 1 is (3x + 2y)°, the measure of angle 2 is 9y°, and the measure of

angle 3 is (x + y)°. Find x and y.

16) The manager of a bulk foods establishment sells a trail mix for $8 per

pound and premium cashews for $15 per pound. The manager wishes to

make a 35-pound trail mix-cashew mixture that will sell for $14 per

pound. How many pounds of each should be used?

17) A college student earned $7300 during summer vacation working as a

waiter in a popular restaurant. The student invested part of the money at

7% and the rest at 6%. If the student received a total of $458 in interest at

the end of the year, how much was invested at 7%?

18) A retired couple has $160,000 to invest to obtain annual income. They

want some of it invested in safe Certificates of Deposit yielding 6%. The

rest they want to invest in AA bonds yielding 11% per year. How much

should they invest in each to realize exactly $15,600 per year?

19) A certain aircraft can fly 1330 miles with the wind in 5 hours and travel

the same distance against the wind in 7 hours. What is the speed of the

wind?

20) Julie and Eric row their boat (at a constant speed) 40 miles downstream

for 4 hours, helped by the current. Rowing at the same rate, the trip back

against the current takes 10 hours. Find the rate of the current.

21) Khang and Hector live 88 miles apart in southeastern Missouri. They

decide to bicycle towards each other and meet somewhere in between.

Hector's rate of speed is 60% of Khang's. They start out at the same time

and meet 5 hours later. Find Hector's rate of speed.

22) Devon purchased tickets to an air show for 9 adults and 2 children. The

total cost was $252. The cost of a child's ticket was $6 less than the cost of

an adult's ticket. Find the price of an adult's ticket and a child's ticket.

23) On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of

jewelry: a number of bracelets at $8 each and a number of necklaces at

$11 each. She wrote a check for $1140 to pay for the order. How many

bracelets and how many necklaces did Rosaria purchase?

24) Natasha rides her bike (at a constant speed) for 4 hours, helped by a

wind of 3 miles per hour. Pedaling at the same rate, the trip back against

the wind takes 10 hours. Find find the total round trip distance she

traveled.

25) A barge takes 4 hours to move (at a constant rate) downstream for 40

miles, helped by a current of 3 miles per hour. If the barge's engines are

set at the same pace, find the time of its return trip against the current.

26) Doreen and Irena plan to leave their houses at the same time, roller

blade towards each other, and meet for lunch after 2 hours on the road.

Doreen can maintain a speed of 2 miles per hour, which is 40% of Irena's

speed. If they meet exactly as planned, what is the distance between

their houses?

27) Dmitri needs 7 liters of a 36% solution of sulfuric acid for a research

project in molecular biology. He has two supplies of sulfuric acid

solution: one is an unlimited supply of the 56% solution and the other

an unlimited supply of the 21% solution. How many liters of each

solution should Dmitri use?

28) Chandra has 2 liters of a 30% solution of sodium hydroxide in a

container. What is the amount and concentration of sodium hydroxide

solution she must add to this in order to end up with 6 liters of 46%

solution?

29) Jimmy is a partner in an Internet-based coffee supplier. The company

offers gourmet coffee beans for $12 per pound and regular coffee beans

for $6 per pound. Jimmy is creating a medium-price product that will

sell for $8 per pound. The first thing to go into the mixing bin was 10

pounds of the gourmet beans. How many pounds of the less expensive

regular beans should be added?

30) During the 1998-1999 Little League season, the Tigers played 57 games. They lost 21 more games than they won. How many games did they win that season?

31) The perimeter of a rectangle is 48 m. If the width were doubled and the

length were increased by 24 m, the perimeter would be 112 m. What are

the length and width of the rectangle?

32) The perimeter of a triangle is 46 cm. The triangle is isosceles now, but if

its base were lengthened by 4 cm and each leg were shortened by 7 cm, it

would be equilateral. Find the length of the base of the original triangle.

33) The side of an equilateral triangle is 8 inches shorter than the side of a

square. The perimeter of the square is 46 inches more than the perimeter

of the triangle. Find the length of a side of the square.

34) The side of an equilateral triangle is 2 inches shorter than the side of a

square. The perimeter of the square is 30 inches more than the perimeter

of the triangle. Find the length of a side of the triangle.

Topic 1: If Only I Had a System ...

This will be your opportunity to be the teacher. Click on "View Full Description and attachments" below for the directions and questions. Be sure to open the file that says "MATH110 Read This First" before you jump in!

Read the attached files. First read the one entitled "MATH110 Read this first," and then open the file called "Systems of Equations Problems with Answers."

Pick ONE of the problems that has not already been solved, and demonstrate its solution using either the substitution or elimination method.

Click Start a New Conversation and make the problem number and topic (#10 Jarod and the Bunnies) the subject of your post.

The answers are at the end of the file, so don't just give an answer—we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!

This is a moderated forum. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order to get credit.

I will indicate in the grading comments if corrections need to be made. If you haven't received credit, first double-check for my comments in the gradebook. If everything looks OK, then Message me asking me to check on it.

You must make the necessary corrections and have your work posted in order to receive credit.

Your initial post is worth 10 points. It is not necessary to respond to 2 classmates on this forum, although a request for clarification on the procedure used would be appropriate. Also, I'm sure that a "Thank You" for an exceptionally clear explanation would be welcome!

Please sign ALL your Forum posts with the name that you like to be called - it makes it so much easier for the rest of us to address you by your preferred name when we respond.

Questions:

Systems of Equations

1) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot

dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot

dogs and 4 bags of potato chips for $9.25. Find the cost of each item.

2) University Theater sold 556 tickets for a play. Tickets cost $22 per adult

and $12 per senior citizen. If total receipts were $8492, how many senior

citizen tickets were sold?

3) A tour group split into two groups when waiting in line for food at a fast

food counter. The first group bought 8 slices of pizza and 4 soft drinks

for $36.12. The second group bought 6 slices of pizza and 6 soft drinks

for $31.74. How much does one slice of pizza cost?

4) Tina Thompson scored 34 points in a recent basketball game without

making any 3-point shots. She scored 23 times, making several free

throws worth 1 point each and several field goals worth two points each.

How many free throws did she make? How many 2-point field goals did

she make?

5) Julio has found that his new car gets 36 miles per gallon on the highway

and 31 miles per gallon in the city. He recently drove 397 miles on 12

gallons of gasoline. How many miles did he drive on the highway? How

many miles did he drive in the city?

6) A textile company has specific dyeing and drying times for its different

cloths. A roll of Cloth A requires 65 minutes of dyeing time and 50

minutes of drying time. A roll of Cloth B requires 55 minutes of dyeing

time and 30 minutes of drying time. The production division allocates

2440 minutes of dyeing time and 1680 minutes of drying time for the

week. How many rolls of each cloth can be dyed and dried?

7) A bank teller has 54 $5 and $20 bills in her cash drawer. The value of the

bills is $780. How many $5 bills are there?

8) Jamil always throws loose change into a pencil holder on his desk and

takes it out every two weeks. This time it is all nickels and dimes. There

are 2 times as many dimes as nickels, and the value of the dimes is $1.65

more than the value of the nickels. How many nickels and dimes does

Jamil have?

9) A flat rectangular piece of aluminum has a perimeter of 60 inches. The

length is 14 inches longer than the width. Find the width.

10) Jarod is having a problem with rabbits getting into his vegetable garden,

so he decides to fence it in. The length of the garden is 8 feet more than 3

times the width. He needs 64 feet of fencing to do the job. Find the

length and width of the garden.

11) Two angles are supplementary if the sum of their measures is 180°. The

measure of the first angle is 18° less than two times the second angle.

Find the measure of each angle.

12) The three angles in a triangle always add up to 180°. If one angle in a

triangle is 72° and the second is 2 times the third, what are the three

angles?

13) An isosceles triangle is one in which two of the sides are congruent. The

perimeter of an isosceles triangle is 21 mm. If the length of the

congruent sides is 3 times the length of the third side, find the

dimensions of the triangle.

14) A chemist needs 130 milliliters of a 57% solution but has only 33% and

85% solutions available. Find how many milliliters of each that should be

mixed to get the desired solution.

15) Two lines that are not parallel are shown. Suppose that the measure of

angle 1 is (3x + 2y)°, the measure of angle 2 is 9y°, and the measure of

angle 3 is (x + y)°. Find x and y.

16) The manager of a bulk foods establishment sells a trail mix for $8 per

pound and premium cashews for $15 per pound. The manager wishes to

make a 35-pound trail mix-cashew mixture that will sell for $14 per

pound. How many pounds of each should be used?

17) A college student earned $7300 during summer vacation working as a

waiter in a popular restaurant. The student invested part of the money at

7% and the rest at 6%. If the student received a total of $458 in interest at

the end of the year, how much was invested at 7%?

18) A retired couple has $160,000 to invest to obtain annual income. They

want some of it invested in safe Certificates of Deposit yielding 6%. The

rest they want to invest in AA bonds yielding 11% per year. How much

should they invest in each to realize exactly $15,600 per year?

19) A certain aircraft can fly 1330 miles with the wind in 5 hours and travel

the same distance against the wind in 7 hours. What is the speed of the

wind?

20) Julie and Eric row their boat (at a constant speed) 40 miles downstream

for 4 hours, helped by the current. Rowing at the same rate, the trip back

against the current takes 10 hours. Find the rate of the current.

21) Khang and Hector live 88 miles apart in southeastern Missouri. They

decide to bicycle towards each other and meet somewhere in between.

Hector's rate of speed is 60% of Khang's. They start out at the same time

and meet 5 hours later. Find Hector's rate of speed.

22) Devon purchased tickets to an air show for 9 adults and 2 children. The

total cost was $252. The cost of a child's ticket was $6 less than the cost of

an adult's ticket. Find the price of an adult's ticket and a child's ticket.

23) On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of

jewelry: a number of bracelets at $8 each and a number of necklaces at

$11 each. She wrote a check for $1140 to pay for the order. How many

bracelets and how many necklaces did Rosaria purchase?

24) Natasha rides her bike (at a constant speed) for 4 hours, helped by a

wind of 3 miles per hour. Pedaling at the same rate, the trip back against

the wind takes 10 hours. Find find the total round trip distance she

traveled.

25) A barge takes 4 hours to move (at a constant rate) downstream for 40

miles, helped by a current of 3 miles per hour. If the barge's engines are

set at the same pace, find the time of its return trip against the current.

26) Doreen and Irena plan to leave their houses at the same time, roller

blade towards each other, and meet for lunch after 2 hours on the road.

Doreen can maintain a speed of 2 miles per hour, which is 40% of Irena's

speed. If they meet exactly as planned, what is the distance between

their houses?

27) Dmitri needs 7 liters of a 36% solution of sulfuric acid for a research

project in molecular biology. He has two supplies of sulfuric acid

solution: one is an unlimited supply of the 56% solution and the other

an unlimited supply of the 21% solution. How many liters of each

solution should Dmitri use?

28) Chandra has 2 liters of a 30% solution of sodium hydroxide in a

container. What is the amount and concentration of sodium hydroxide

solution she must add to this in order to end up with 6 liters of 46%

solution?

29) Jimmy is a partner in an Internet-based coffee supplier. The company

offers gourmet coffee beans for $12 per pound and regular coffee beans

for $6 per pound. Jimmy is creating a medium-price product that will

sell for $8 per pound. The first thing to go into the mixing bin was 10

pounds of the gourmet beans. How many pounds of the less expensive

regular beans should be added?

30) During the 1998-1999 Little League season, the Tigers played 57 games. They lost 21 more games than they won. How many games did they win that season?

31) The perimeter of a rectangle is 48 m. If the width were doubled and the

length were increased by 24 m, the perimeter would be 112 m. What are

the length and width of the rectangle?

32) The perimeter of a triangle is 46 cm. The triangle is isosceles now, but if

its base were lengthened by 4 cm and each leg were shortened by 7 cm, it

would be equilateral. Find the length of the base of the original triangle.

33) The side of an equilateral triangle is 8 inches shorter than the side of a

square. The perimeter of the square is 46 inches more than the perimeter

of the triangle. Find the length of a side of the square.

34) The side of an equilateral triangle is 2 inches shorter than the side of a

square. The perimeter of the square is 30 inches more than the perimeter

of the triangle. Find the length of a side of the triangle.