Question

Sara is selling tickets to a high school festival. She sold 10 less senior tickets than junior tickets and she sold 3 times as many sophomore tickets as junior tickets (no freshman allowed). Senior tickets cost $3, junior tickets cost $5 and sophomore tickets cost $7. Sara raised $782. Write an equation to model the situation so that we can find the amount of tickets sold to seniors, juniors, and sophomores.

Answer 1

`29x-30=782` where x denotes number of junior tickets.

Explanation:

Let x denotes number of junior tickets.

Sara sold 10 less senior tickets than junior tickets.

Number of senior tickets
`=x-10`

Sara sold 3 times as many sophomore tickets as junior tickets.

Number of sophomore tickets
`=3x`

Senior tickets cost $3, junior tickets cost $5 and sophomore tickets cost $7.

Total amount raised by Sara
`=5x+3(x-10)+7(3x)=5x+3x-30+21x=29x-30`

Sara raised $782.

So,

`29x-30=782`