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?

The number of pens = 120 and the number of pencils = 200

Step-by-step explanation:

Let the number of pens x, and the number of pencils is y

the cost of one pen $1, and the cost of one pencil $0.5

The cost of the whole purchase was $220

1 * x + 0.5 * y = 220

x + 0.5 y = 220 ⇒ eq. (1)

there were 80 more pencils than pens

y - x = 80 ⇒ eq. (2)

from eq. (2) x = y - 80

By substitution with x from the last equation at eq. (1)

∴ (y - 80) + 0.5 y = 220

1.5y = 220 + 80 = 300

y = 300/1.5 = 200

x = y - 80 = 200 - 80 = 120

So, the number of pens = 120 and the number of pencils = 200