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Participation Activity \#6 This is similar to Try It \#8 in the OpenStax text. Meal tickets at the circus cost \( \$ 4.00 \) for children and \( \$ 12.00 \) for adults. If 1,650 meal tickets were bought for a total of \( \$ 14,200 \), how many children and how many adults bought meal tickets? Enter the exact answers. The number of adult meal tickets sold was Number The number of child meal tickets sold was Number

Ask by Bernard Hamilton. in the United States
Feb 27,2025

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Answer

950 adult meal tickets and 700 child meal tickets were sold.

Solution

Let a be the number of adult tickets and c be the number of children tickets. We have:   c + a = 1650        (1)   4c + 12a = 14200      (2) Solve equation (1) for c:   c = 1650 − a Substitute into equation (2):   4(1650 − a) + 12a = 14200   6600 − 4a + 12a = 14200   6600 + 8a = 14200 Solve for a:   8a = 14200 − 6600   8a = 7600   a = 950 Now substitute back to find c:   c = 1650 − 950 = 700 Thus, the number of adult meal tickets sold was 950, and the number of child meal tickets sold was 700.

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Beyond the Answer

To solve this problem, we can set up a system of equations based on the information given. Let \( x \) be the number of adult meal tickets and \( y \) be the number of child meal tickets. We have two equations: 1. \( x + y = 1650 \) (total number of tickets) 2. \( 12x + 4y = 14200 \) (total cost) Now, we can use the first equation to express \( y \) in terms of \( x \): \( y = 1650 - x \) Substituting this into the second equation: \( 12x + 4(1650 - x) = 14200 \) This simplifies to: \( 12x + 6600 - 4x = 14200 \) Combining like terms gives: \( 8x + 6600 = 14200 \) Subtracting \( 6600 \) from both sides results in: \( 8x = 7600 \) Dividing both sides by \( 8 \): \( x = 950 \) (the number of adult meal tickets sold) Now substituting back to find \( y \): \( y = 1650 - 950 \) Thus, \( y = 700 \) (the number of child meal tickets sold) So, the final answers are: The number of adult meal tickets sold was 950. The number of child meal tickets sold was 700.

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