Question

Chara sold 52 boxes of candy for her marching band fundraiser. The large box costs $3.50 each and the small box costs $1.75 each. If Chara sold $112 worth of candy, how many boxes of each size did she sell?

Answer 1

The number of boxes of candy sold are:

40 small boxes and

12 large boxes of candy.

Explanation:

Let the number of small boxes sold = x

Let the number of large boxes sold = y

we are given the following information:

x + y = 52 - - - - - -(1) (Chara sold 52 boxes of candy)

3.5(y) + 1.75(x) = 112 - - - - - - (2) (Chara sold $112 worth of candy)

From the two equations above, x and y can be solved as follows:

x + y = 52 - - - - - -(1)

x = 52 - y - - - - - - (3)

putting the value if x in equation (3) to replace x in equation (2);

3.5(y) + 1.75(x) = 112 - - - - - - (2)

3.5(y) + 1.75(52 - y) = 112

3.5y + 91 - 1.75y = 112

(3.5y - 1.75y) + 91 = 112

1.75y = 112 - 91 = 21

y = 21 ÷ 1.75 = 12

y = 12

Now, let us put the value of y into equation (3)

x = 52 - y - - - - - - (3)

x = 52 - 12 = 40

Therefore,

40 small boxes and 12 large boxes of candy were sold.