problem solving

Question

Katie bought some pens for $2.00 each and some pencils for 50 cents each. She bought twice as many pens as pencils and spent a total of $13.50. How many of each did she buy? Show how you got the answer

Answer 1

Let x = number of pencils, y = #pens

y = 2x (number of pens is twice the number of pencils)

50x + 200y = 1350 (work in cents instead of dollars, each pencil costs 50 cents, each pen 200 cents)

Now use substitution (replace y with 2x in the 2nd equation):

50x + 200(2x) = 1350

50x + 400x = 1350

450x = 1350

x = 3 (#pencils) (1350/450 = 3)

y = 6 (#pens) (y = 2x, y= 2(3))

Check:

Number of pens (6) is twice number of pencils (3)

6 pens cost $12 (6 times $2 per pen)

3 pencils cost $1.50 ( 3 times $.50)

Total amount spent $12 + $1.50 = $13.50.