Question

The school that Beth goes to is selling tickets to a spring musical. On the first day of ticket sales

the school sold 2 senior citizen tickets and 7 student tickets for a total of $106. The school took
in $208 on the second day by selling 3 senior citizen tickets and 14 student tickets. Find the price
of a senior citizen ticket and the price of a student ticket.

Answer 1

Student tickets are $14 each

Senior Citizen tickets are $4 each

Explanation:

Let C be the price of a Senior Citizen ticket, and S be the price of a Student ticket.

We learn that on the first day:

2C + 7S = $106

On the second day:

3C + 14S = $208

We have two equations and two unknowns. Rearrange either equation to isolate either C or S and use that value in the other equation.

I'll choose 2C + 7S = $106

C = ($106 - 7S)/2

Use this in the other equation:

3C + 14S = $208

3(($106 - 7S)/2) + 14S = $208

($318 - 21S)/2 + 14S = $208

$159 - 10.5S + 14S = $208

3.5S = $49

S = $14 Student tickets are $14 each

Use this answer in either equation to find C:

C = ($106 - 7S)/2

C = ($106 - 7($14))/2

C = $4 Senior Citizen tickets are $4 each

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Check to see if these values work in the original equations:

1. 2C + 7S = $106

2($4) + 7($14) = $106 ?

$8 + $98 = $106 ? YES

2. 3C + 14S = $208

3($4) + 14($14) = $208 ?

$12 + $196 = $208 ? YES