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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?

Respuesta :

Edufirst

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

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