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How do you do this problem?

How do you do this problem?-example-1

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Answer:

An adult ticket costs $4. A child ticket costs $7.

Explanation:

We want to find out the price of an adult ticket and the price of a child ticket. The unknowns in this problem are those two prices. Since they are unknown, we will choose a variable to represent each unknown.

Let a = price of one adult ticket

Let c = price of one child ticket

3 adult tickets and 9 child tickets sold for $75.

3 adult tickets cost 3a. 9 child tickets cost 9c. Together they cost 3a + 9c. They cost $75, so our first equation is

3a + 9c = 75

8 adult tickets and 5 child tickets sold for $67.

8 adult tickets cost 8a. 5 child tickets cost 5c. Together they cost 8a + 5c. They cost $67, so our second equation is

8a + 5c = 67

We have a system, of equations:

3a + 9c = 75

8a + 5c = 67

We will use the addition method and cancel out a. Multiply the first equation by -8. Multiply the second equation by 3.

-24a - 72c = -600

24a + 15c = 201

Add the two equations just above.

-57c = -399

c = 7

Now substitute c = 7 in the first original equation and solve for a.

3a + 9c = 75

3a + 9(7) = 75

3a + 63 = 75

3a = 12

a = 4

An adult ticket costs $4. A child ticket costs $7.

User Adrian Nowicki
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