Question

A school club sold 220 T-shirts for a fundraiser. Adult-size shirts cost $20 each and child-size shirts cost $15 each. The total collected for all the T-shirts sold was $3,550.

How many adult-size T-shirts were sold?

Answer 1

The answer is "50 adult size t-shirts".

total t-shirts = 220
cost of adult size t-shirt = $20
and cost of child size t-shirt = $15
total money collected when all the T-shirts were sold = $3,550
let x is the number of adult size t-shirts
and y is the number of child size t-shirts, then
x + y = 220
y = 220 - x
and 20x + 15y = $3,550
Now replace y with 220 - x
20x + 15(220 - x) = 3550
20x + 3300 -15x = 3550
20x -15x = 3550 - 3300
5x = 250
x = 50
and y = 220 - x = 220 - 50 = 170
Thus 50 adult size t-shirts were sold.

Answer 2

Assume that the number of adult-size shirts is x and the number of child-size shirts is y.

We are given that:
(1) Total number of T-shirts sold is 220, this means that:
x + y = 220
This can be rewritten as:
x = 220-y ..........> equation I
(2) Adult-sized shirts cost $20, child-sized shirts cost $15 and the total collected money was $3550, this means that:
20x + 15y = 3550 ........> equation II

Substitute with equation I in equation II as follows:
20x + 15y = 3550
20 (220-y) + 15y = 3550
4400 - 20y + 15y = 3550
4400 - 3550 = 20y - 15y
850 = 5y
y = 850/5
y = 170

Substitute with y in equation I to get x as follows:
x = 220-y
x = 220-170 = 50

Based on the above calculations,
number of adult-sized T-shirts = x = 50 T-shirts
number of child-sized T-shirts = y = 170 T-shirts