# Systems of Linear Equations

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## Systems of Linear Equations Answer Key

1.

The school drama group sells tickets to a play. The tickets cost $6.50 for students or $9.25 for adults. There are 370 people who buy tickets and the sales total $2968.75. How many students and how many adults purchased tickets?

- [math]6.5s+9.25a=2968.75[/math]

[math]s+a=370[/math]

165 Students

205 Adults

2.

Colin has 85 coins which are a mixture of nickels and quarters that are worth $19.25.

How many nickels?

How many quarters?

Show your work.

How many nickels?

How many quarters?

Show your work.

- [math]n+q=85[/math]

[math].05n+.25q=19.25[/math]

10 Nickels

75 Quarters

3.

The sum of the digits in a double digit number is 9. The difference of the first digit subtracted from the second digit is 3. Use a system of linear equations to solve and show your work. What is the original double digit number?

- [math]x+y=9[/math]

[math]y-x=3[/math]

36

4.

Two schools order balls for their PE departments from the same supplier. School A orders 14 basketballs and 18 footballs for a total cost of $1800.40. School B orders 32 basketballs and 2 footballs for a total cost of $1676.60.

What is the cost of a basketball?

What is the cost of a football?

What is the cost of a basketball?

What is the cost of a football?

- [math]14x+18y=1800.4 [/math]

[math]32x+2y=1676.6[/math]

Basketball = $48.50

Football = $62.30

5.

The sum of the digits in a double digit number is 10. The difference of the second digit subtracted from the first digit is 2. Use a system of linear equations to solve and show your work. What is the number?

- [math]x+y=10 , x-y=2[/math]

64

6.

When Zantia went to the mall there was a sale on shirts for $14.50 and jeans for $45.37. She bought 8 items and paid $208.61 before taxes. Use a system of linear equations to solve and show your work. How many shirts and how many jeans did Zantia buy?

- [math]x+y=8[/math]

[math]14.5x+45.37y=208.61[/math]

5 shirts and 3 jeans

7.

A landscaping company orders 10 shrubs and 2 trees for total cost of $730.50. The next week they make another order of 6 shrubs and 4 trees for a total of $784.10. Use a system of linear equations to solve and show your work.

How much did the shrubs cost?

How mush did the trees cost?

How much did the shrubs cost?

How mush did the trees cost?

- [math]10s+2t=730.5[/math]

[math]6s+4t=784.1[/math]

Shrubs = $48.35

Trees - $123.50

8.

Two hot air balloons are flying at the same time. The first balloon begins at 1,800 ft and descends to the ground in 20 minutes. The second balloon begins at 200 ft and ascends to 1,600 ft in 20 minutes. Are the balloons ever at the same altitude at the same time? If so when and at what altitude? Use a system of linear equations to solve and show your work.

- [math]1800-(1800/20)A=200+((1600-200)/20)A[/math]

Yes. After 10 minutes they are both at 900 ft.

9.

There are 2 different sized jugs in the kitchen. Three of the small jugs plus two of the large jugs hold a total of 24 cups. If a full large jug is used to fill a small jug there will 2 cups left in the large jug. How many cups does the small jug hold?

- [math]3s+2l=24[/math]

[math]l-s=2[/math]

The small jug hold 4 cups.

10.

Allison opens a bank account and deposits $100. She commits to adding $30 per week to build her savings. Shaniqua starts a savings account at the same time, deposits $50 and commits to adding $45 per week. Will Shaniqua ever have more money in the bank than Allison? If so after how many weeks will this happen?

- [math]100+30w=50+45w[/math]

[math]w=3.3[/math]

Yes. After 4 weeks Shaniqua will have more money.

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