Question

A museum charges $12.50 for a one-day youth admission and $17.50 for a one-day adult admission. One Friday, the museum collected $1485 from a total of 106

youths and adults. How many admissions of each type were sold?
UZE

Answer 1

number of youth admissions sold (x) = 74

number of adult admissions sold (y) = 32

Explanation:

Let x = number of youth admissions

Let y = number of adult admissions

Given:

• total number of admissions sold = 106

⇒ x + y = 106

Given:

• cost of youth admission = $12.50
• cost of adult admission = $17.50
• total amount collected = $1485

⇒ 12.5x + 17.5y = 1485

Rewrite x + y = 106 to make y the subject:

⇒ y = 106 - x

Substitute y = 106 - x into 12.5x + 17.5y = 1485 and solve for x:

⇒ 12.5x + 17.5(106 - x) = 1485

⇒ 12.5x + 1855 - 17.5x = 1485

⇒ 5x = 370

⇒ x = 74

Substitute found value of x into y = 106 - x to find y:

⇒ y = 106 - 74

⇒ y = 32