Question

Four hundred vouchers were sold for a carwash. Vouchers to wash trucks were $4, while vouchers to wash compact cars were $3. If the total sales were $1350, how many of each type of voucher were sold?

Answer 1

150 vouchers to wash trucks were sold

250 vouchers to wash compact cars were sold

Explanation:

Here, we are interested in calculating the number of each type of vouchers sold.

Let the number of vouchers to wash trucks be x while the number of vouchers to wash compact trucks be y.

Firstly, we know that both sums up to be 400.

Mathematically;

x + y = 400 •••••••••(i)

Secondly,

since a voucher to wash trucks sell $4, and we sold a total of x, the amount generated from selling is 4 * x = $4x

Same way for the vouchers to wash compact cars, we have a total of $3 * y = $3y

The sum of both gives $1350, which is the total sales.

Mathematically;

4x + 3y = 1350 ••••••(ii)

So we have two equations to solve simultaneously;

x + y = 400

4x + 3y = 1350

Multiply equation i by 4 , we have;

4x + 4y = 1600

4x + 3y = 1350

Subtract equation ii from i, we have 4y-3y = 1600-1350

y = 250

From equation 1, we know that

x + y = 400

This means that;

x = 400 -y

x = 400 -250

x = 150