How many passes sold?

Question

A ski resort charges $80 for adult all-day passes and $35 for children's all-day passes. On a particular day, they made $59,095 in sales. They also know that they sold 809 passes altogether.

How many adult passes were sold?

How many children's passes were sold?

Answer 1

Two equations are needed to solve this question.

Let x = the number of adult passes, and y = the number of child passes

 

1. x + y = 809 passes

 

2. $80x + $35y = $59095

 

solve equation 1 for x, which yields x = 809 - y

 

substitute the value for x in equation 2, which becomes

$80(809 - y) +$35y = $59095

we get $64720 - $80y - $35y = $59095

combining, we get -$45y = -$5625; multiply both sides by -1 to get

$45y = $5625

solving, we get y = 125 passes

 

subtracting, we get 809 passes - 125 passes = 684 passes

 

so. our answers are 684 adult passes and 125 child passes

 

Proof: 684 adult passes times $80/adult pass + 125 child passes times $35/child pass = $59095

$54720 + $4375 = $59095