Write and solve systems of linear equations

Problem #1: Two customers went to a grocery store to buy apples and bananas. Each apple costs the same amount, and each banana costs the same amount.

The first customer paid $12.10 for 10 apples and 6 bananas.

The second customer paid $15.95 for 11 apples and 9 bananas.

What was the cost in dollars of each banana?

Mathematical Equivalence

OFF

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AI.9.2.I

Problem #2: Karol and her friends went to the carnival on Friday and Saturday.

On Friday, they bought 3 hot dogs and 2 sodas for $9.00.

On Saturday, they purchased 4 hot dogs and 5 sodas for $13.75.

If the price of the hot dog and soda were the same on each day, what was the cost of each hot dog?

Mathematical Equivalence

ON

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AI.9.2.I

The Community Theater collected $4,355 in ticket sales for their spring production.

Each adult ticket costs $8.

Each student ticket costs $5.

If the total number of tickets sold was 724, how many adult tickets were sold?

Mathematical Equivalence

ON

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AI.9.2.I

Color copies are printed at two different businesses. The cost of copies at each business is shown.

Quick Copy charges an initial fee of $5.00 plus $0.55 per copy

Write an equation to model this situation.

Mathematical Equivalence

ON

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AI.9.2.B

Copy Palace charges an initial fee of $10.00 plus $0.45 per copy.

Write an equation to model this situation.

Mathematical Equivalence

ON

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AI.9.2.B

Using the two equations you have already written, solve the following problem...

Color copies are printed at two different businesses.

The cost of copies at each business is shown.

Quick Copy charges an initial fee of $5.00 plus $0.55 per copy.

Copy Palace charges an initial fee of $10.00 plus $0.45 per copy.

After how many copies will the total cost of printing be equal at the two businesses?

Mathematical Equivalence

ON

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AI.9.2.I

The two types of tickets sold at a baseball game are standard tickets and discounted tickets. The price of a discounted ticket was 80% of the price of a standard ticket.

There were 153 standard tickets sold at the baseball game.

There were 47 discounted tickets sold at the baseball game.

The total amount of ticket sales from the standard and discounted tickets was $2,649.34

The line graphed on the grid represents the first equation in a system of linear equations for this situation.

If the second equation in the system is y=0.80x, what is the best estimate of the price of a discounted ticket?

• $13.95

• $14.55

• $13.25

• $11.15

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AI.9.2.I