Question

Amy sold pens and pencils for a fundraiser at school. Pencils sold for $1.50 and pens sold for $2. She sold a total of 35 items and made $61.50. How many pens did Amy sell?

Answer 1

Let's break this down into a system of equations.
Let d = number of pencils, and p = number of pens.
We want to solve for p.
These are our two equations:
1) 1.50d + 2p = 61.50.
She sold $61.50 in merchandise, $1.50/pencil, $2/pen
2) d + p = 35
She sold a total of 35 items.
To solve for p, let's write equation p a different way:
3) d= 35 - p
Now we can substitute d from equation 3) into equation 1) to figure out the answer.
1.50 (35 - p) + 2p = 61.5
52.5 - 1.5p + 2p = 61.5 Distribute within parentheses
52.5 + .5p = 61.5 Subtract 52.5 from each side
.5p = 9 Multiply both sides by 2
p = 18
p = 18
Amy sold 18 pens. To find how many pencils she sold:
p + d = 35
18 + d = 35
d = 17

Answer is 18 pens.