Question

A gym is in the process of purchasing new 5-pound and 8-pound dumbbells for their aerobics room. Each 5-pound dumbbell costs $8 and each 8-pound dumbbell costs $12. The entire shipment of dumbbells costs $432 and weighs 282 pounds. Which equations can be used to find the number of 5-pound dumbbells, x, and the number of 8-pound dumbbells, y, in the shipment?

Answer 1

The equations that can be used to find the number of 5 pound dumbbells and 8 pound dumbbells are: x + y = 282 and 8x + 12y = 432

Answer 2

Let f=number of five pound and e=number of eight pound dumbbells

5f+8e=282

8e=282-5f

e=(282-5f)/8

...

8f+12e=432, using e found above

8f+12(282-5f)/8=432

64f+12(282-5f)=3456

64f-60f+3384=3456

4f+3384=3456

4f=72

f=18, since e=(282-5f)/8

e=24

So there are 18 five pound and 24 eight pound dumbbells in the shipment.