Question

Imani's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 7

senior citizen tickets and 4 student tickets for a total of $104. The school took in $68 on the

second day by selling 7 senior citizen tickets and 1 student ticket. Find the price of a senior

citizen ticket and the price of a student ticket.

Answer 1

$8 for Senior Citizens

$12 for Students

Explanation:

Let C be the price of a senior citizen ticket

Let S be the price of a student ticket.

We are told that, on the first day, that:

7C + 4S = $104

On the second day:

7C + 1S = $68

We have 2 equations and 2 unknowns. Rearrange either equation to express one of the unknowns in terms of the other

For example:

7C + 1S = $68

S = $68 - 7C

Now use this value of S in the other equation:

7C + 4S = $104

7C + 4($68 - 7C) = $104

7C + $272 - 28C = $104

-21C = - $168

C = $8 for a Senior Citizen ticket

We can use C = $8 in either equation to find S.

S = $68 - 7C

S = $68 - 7($8)

S = $12

Student tickets are $8 each

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See if these values work in the original equations:

1. 7C + 4S = $104

7($8) + 4($12) = $104 ?

$56 + $48 = $104 YES

2. 7C + 1S = $68

7($8) + 1($12) = $68 ?

$56 + $12 = $68 YES