A kid has just enough money to buy either 5 erasers and 30 pencils or 10 erasers and 24 pencils. Each eraser costs $0.30. How much does each pencil cost

Question

Use multiplication, division, subtraction, or addition to answer this.

Answer 1

The instructions say to “ use multiplication, division, subtraction, or addition to answer this,” but the most important (and, usually, the most difficult) is to correctly translate the words into math expressions.

Let’s assign variables:
      E = the cost of an eraser
      P – the cost of a pencil

Getting the units correct is important:
            Cost-per-eraser * number-of-erasers   = cost-of-all-erasers

“Either” means that the two choices cost the same total amount (“just enough money”)

So,
       5*E  +  30*P     =    10*E  +  24*P
  And  

            E = $0.30

      5*($0.30) + 30*P   =  10*(($0.30)  +24*P

Let’s use cents to solve this, then convert back to dollars:
           150  + 30P = 300 + 24P
           150 +  6P  = 300             (subtracted 24P from both sides)
             6P  = 150                (subtracted 150 from both sides)
                 P  = 25                 (divided both sides by 6)

Converting cents back to dollars:   The price of a pencil is $0.25.

Checking:
    Is 5*(30) + 30*(25)  = 10*(30) + 24*(25)        ?
         150 +  750   =  300 + 600
              900   =   900         Yes.