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Elisa's school is selling tickets to a choral performance.

On the first day of ticket sales, the school sold 8 senior citizen tickets and 5 child tickets for a total of $94.

On the second day, the school took in $152 by selling 4 senior citizen tickets and 10 child tickets.

What is the price of one senior citizen ticket and one child ticket?

Answer :

Let's define the next variables:

x: price of one senior ticket

y: the price of one child ticket

On the first day of ticket sales, the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. That is:

8x + 5y = 94 (eq. 1)

The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. That is:

4x + 10y = 152 (eq. 2)

Multiplying equation 2 by 2, we get:

2(4x + 10y) = 2*152

8x + 20y = 304 (eq. 3)

Subtracting equation 1 to equation 3, we get:

8x + 20y = 304

-

8x + 5y = 94

------------------------

15y = 210

y = 210/15

y = 14

Substituting this result into equation 1:

8x + 5(14) = 94

8x + 70 = 94

8x = 94 - 70

8x = 24

x = 24/8

x = 3

Each senior citizen ticket cost $3 and each child ticket cost $14

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