Question

A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens and pencils were purchased if there were 80 more pencils than pens?

Answer 1

120 pens and 200 pencils

Explanation:

Let the number of pencils bought be x while pens will be y.

Cost

Considering that a pen costs $1 then for y pens, the cost will be y*$1=$y

The pencils cost $0.5 then for x pencils the cost will be $0.5*x=$0.5x

Total cost is $220 hence expressed as

0.5x+y=220

Quantity

Since the number of pencils, x were more than number of pens, y by 80 pieces then

x=80+y

Since we initially had the equation 0.5x+y=220 then we substitute x with 80+y hence

0.5(80+y)+y=220

40+0.5y+y=220

1.5y+40=220

1.5y=220-40=180

y=180/1.5=120

Since x=y+80 and y is found to be 120 then

x=120+80=200