Question

The school that Danielle goes to is selling tickets to a choir concert. On the first day of ticket sales the school sold 14 adult tickets and 6 student tickets for a total of $190. The school took in $252 on the second day by selling 12 adult tickets and 12 student tickets. What is the price of an adult ticket and the price of a student ticket?

Answer 1

The price of an adult ticket = $13.3

The price of a student ticket = $7.7

Substitution equations

On the first day of ticket sales = 14a + 6s =$190

On the second day of ticket sales = 12a + 12s =$252

From equation two, make a the subject of formula

Therefore,

$a = \frac{252 - 12s}{12}$

Use this form for substitution into equation one.

That is,

$14( \frac{252 - 12s}{12} ) + 6s = 190$

$14(252 - 12s) + 6s = 190 \times 12$

$3528 - 168s + 6s = 2280$

$- 168s + 6s = 2280 - 3528$

$- 162s = - 1248$

$s = \frac{ - 1248}{ - 162}$

$s = 7.7$

Therefore, the price of a student ticket = $7.7

To solve for a, substitute s = 7.7 in equation two

That is,

$12a + 12(7.7) = 252$

$12a + 92.4 = 252$

$12a = 252 - 92.4$

$12a = 159.6$

$a = \frac{159.6}{12}$

$a = 13.3$

Therefore, the price of an adult ticket = $13.3

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