Question

1. work required for full credit! (a.ei.2, 10 points)

the school that ming goes to is selling tickets to a play. on the first day of ticket sales the school
sold 7 senior citizen tickets and 10 child tickets for a total of $183. the school took in $150 on th
second day by selling 14 senior citizen tickets and 2 child tickets. what is the price each of one
senior citizen ticket and one child ticket?
a) senior citizen ticket: $5, child ticket: $9 b) senior citizen ticket: $13, child ticket: $14
c) senior citizen ticket: $7, child ticket: $6 d) senior citizen ticket: $9, child ticket: $12

Explanation:

Step1: Define Variables

Let \( s \) be the price of a senior citizen ticket and \( c \) be the price of a child ticket.

Step2: Set Up Equations

From the first day: \( 7s + 10c = 183 \)
From the second day: \( 14s + 2c = 150 \)
We can simplify the second equation by dividing by 2: \( 7s + c = 75 \), so \( c = 75 - 7s \)

Step3: Substitute \( c \) into First Equation

Substitute \( c = 75 - 7s \) into \( 7s + 10c = 183 \):
\( 7s + 10(75 - 7s) = 183 \)
\( 7s + 750 - 70s = 183 \)
\( -63s = 183 - 750 \)
\( -63s = -567 \)
\( s = \frac{-567}{-63} = 9 \)

Step4: Find \( c \)

Substitute \( s = 9 \) into \( c = 75 - 7s \):
\( c = 75 - 7(9) = 75 - 63 = 12 \)

Step5: Check with Options

We found \( s = 9 \) and \( c = 12 \), which matches option D.

Answer:

D. senior citizen ticket: $9, child ticket: $12