Question

Barb is a huge fan of boy bands. She recently attended a concert of her favorite group, Sis'tem.

Barb bought some souvenirs to remember the experience. She purchased shirts that cost $30
each and keychains that cost $4.50 each
Problem
If Barb bought 7 items and spent $133.50, how many shirts did she buy?

Answer 1

4 shirts and 3 keychains

Explanation:

1 shirt cost $30

So 4 shirts cost 4×30=$120

1 keychain cost $ 4.50

3 keychains cost 4.50×3=$13.50

Total =$120+$13.50=$133.50

Answer 2

4 shirts

Explanation:

An equation can be written that relates the number of items bought and their cost. Let s represent the number of shirts bought. Then (7-s) is the number of keychains. The total cost was ...

30s +4.50(7 -s) = 133.50 . . . . total cost of items bought

25.50s +31.50 = 133.50 . . . . simplify

25.50s = 102.00 . . . . . . . . . . subtract 31.50

s = 102.00/25.50 = 4 . . . . divide by the coefficient of s

Barb bought 4 shirts.

_____

Additional comment

The other 3 items she bought were keychains.

We could write 2 equations using 2 variables:

• s + k = 7
• 30s +4.50k = 133.50

If we solved this by substituting for k, we would have ...

30s +4.50(7 -s) = 133.50 . . . . . the equation we used above