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

Answer:

• 120 pens and 200 pencils.

Explanation:

You can set a system of two equations.

1. Variables

• x: number of pens
• y: number of pencils

2. Cost

• each pen costs $1, then x pens costs: x
• each pencil costs $0.5, then y pencil costs: 0.5y

• Then, the total cost is: x + 0.5y

• The cost of the whole purchase was $ 220, then the first equation is:

          x + 0.5y = 220 ↔ equation (1)

3. There were 80 more pencils than pens

Then:

  pencils  =      80   +   pens

       ↓                               ↓

       y        =      80   +      x        ↔ equation (2)

4. Solve the system

i) Substitute the equation (2) into the equation (1):

• x + 0.5(80 + x) = 220

ii) Solve

• x + 40 + 0.5x = 220

• 1.5x = 180

• x = 180/1.5

• x = 120 pens

iii) Substitute x = 120 into the equation (2)

• y = 80 + 120

• y = 200 pencils

Solution: 120 pens and 200 pencils ← answer