Stephanie's school is selling tickets to a play. On the first day of ticket sales the school sold 4 adult tickets and 10 student tickets for a total of $150. The school took in $105 on the second day by selling 1 adult ticket and 10 student tickets. What is the price each of one adult ticket and one student ticket?

The price of

1 adult ticket = $15

1 student ticket = $9

Step-by-step explanation:

Let

The price of adult tickets be represented by a

The price of student tickets be represented by s

Therefore:

On the first day of ticket sales the school sold 4 adult tickets and 10 student tickets for a total of $150.

4a + 10s = $150 Equation 1

The school took in $105 on the second day by selling 1 adult ticket and 10 student tickets.

a + 10s = $105 Equation 2

a = $105 - 10s

Therefore, we substitute : $105 - 10s = a in Equation 1

4a + 10s = $150 Equation 1

4($105 - 10s) + 10s = $150

$420 - 40s + 10s = $150

Collect like terms

- 40s + 10s = $150 - $420

-30s = -$270

Divide both sides by -30

-30s/-30 = -$270/-30

s = $9

We find a

a = $105 - 10s

a = $105 - 10($9)

a = $105 - $90

a = $15

Therefore, the price of

1 adult ticket = $15

1 student ticket = $9

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step-by-step explanation:

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