Jesse bought 10 more pencils than erasers. A pencil costs $0.15, and an eraser costs $.22. He paid a total of $4.46. How many erasers did Jesse buy?

Question

Jesse bought 10 more pencils than erasers. A pencil costs $0.15, and an eraser costs $0.22. He paid a total of $4.46. How many erasers did Jesse buy?

Answer 1

The key to word (story) problems is to translate the phrases into precise, concise math expressions (variables and operations).

Assign variables :  P = number of pencils
                           E = number of erasers

Note: the problem gives us cost in  $/number  and total $ spent.  To get cost of either pencils or erasers, we multiple $/number by number (leaving just $).

Translate:
   “Jesse bought 10 more pencils than erasers”       means    P = 10 + E
  “A pencil costs $0.15”   means that     $0.15*P was spent on pencils
  “an eraser costs $.22”    means that    $0.22*E was spent on erasers
  “He paid a total of $4.46”    means that   $0.15*P + $0.22*E = $4.46
  “How many erasers did Jesse buy?”     means      report E

Now, the math:

Get rid of P by substituting the first equation into the total one (and solve in cents):
                       15*(10+E)   +   22*E    =   446
                        150 + 37E = 446
                           37E = 296
                               E = 8   Jesse bought 8 erasers

If you want (it’s a good idea), you can solve for P by putting 8 into the first equation:
       P = 10 + E
       P = 10 + 8
       P = 18

Checking:
  Is    18 = 10 + 8    ?   yes

  Is    15*(18) + 22*8  = 446    ?

                 270 + 176  =  446         yes

Answer 2

He bought 8 erasers. 8 erasers would equal 1.76. 

$4.46-1.76=2.70

2.70 divided by .15= 18 

18 pencils is 10 more pencils than erasers. 

I had to use trial and error!