Expert: Chanda Walker - 4/2/2009

Question
I am trying to help my 6th grader with word problems.  I am too old to remember this stuff; would you mind helping?  The problem is: Samantha bought pencils and erasers for school.  She bought a total of 30 items costing $3.78.  If a pencil cost $0.12 and an eraser cost $0.15, how many of each did she buy?  
I feel so dumb when I can't help her on math.  Thank you for any help.

Answer
I'm happy to help.

Let's create some variables.

p = number of pencils
e = number of erasers

p + e = 30   (the total she bought was 30 items)
p* 0.12 + e*0.15 = 3.78   (the number of pencils times their cost plus the number of eraser times their cost sums to 3.78)

Now, we can just use a little substitution and the answer will fall out.

p = 30 - e (from our first equation)

(30 - e)*0.12 +  e*0.15 = 3.78  (substituted into second equation)

3.60 - e*0.12 + e*0.15 = 3.78
(0.15 - 0.12)e = .18
0.03*e = .18
e = 6

She bought 6 erasers.  And so she must have bought 24 pencils.

Let's check that.

24*0.12 = 2.88
6*0.15 = 0.90

2.88+0.90=3.78


Let me know if I can help further.