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Lea's school is selling tickets for the upcoming choral performance. On the first day of the ticket sales, the school sold 10 adult tickets and 10 child tickets for a total of $200. On the second day, the school sold 13 adult tickets and 2 child tickets for a total cost of $172. How much did each child ticket cost?

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Answer: 8

Explanation:

Let's assume that the cost of an adult ticket is A dollars and the cost of a child ticket is C dollars.

From the information given on the first day, we know that 10 adult tickets were sold, so the total cost of adult tickets on the first day is 10A dollars. Similarly, 10 child tickets were sold, so the total cost of child tickets on the first day is 10C dollars. Together, these two amounts add up to $200, so we can write the equation:

10A + 10C = 200

On the second day, 13 adult tickets were sold, so the total cost of adult tickets on the second day is 13A dollars. Additionally, 2 child tickets were sold, so the total cost of child tickets on the second day is 2C dollars. Together, these two amounts add up to $172, so we can write the equation:

13A + 2C = 172

We now have a system of two equations with two unknowns:

10A + 10C = 200

13A + 2C = 172

To solve this system, we can use the method of substitution or elimination. I will use the method of elimination.

Multiplying the first equation by 13 and the second equation by 10, we get:

130A + 130C = 2600

130A + 20C = 1720

Now, let's subtract the second equation from the first equation:

(130A + 130C) - (130A + 20C) = 2600 - 1720

110C = 880

Dividing both sides of the equation by 110, we find:

C = 8

Therefore, each child ticket costs $8.

User Abdul Nasir B A
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