Jaslyn bought 4 home theater systems and 5 water heaters. Each home theater system costs $320 more than each water heater. She spent 20% of her money on the water heaters.
- How much did each home theater system cost?
- How much did she spend altogether?
| |
Home theater systems |
Water heaters |
Total |
| Number |
4 |
5 |
|
| Value |
1 u + $320 |
1 u |
|
| Total value |
4 u + $1280 |
5 u |
|
Comparing amounts
spent on home theater systems
and water heaters |
80%
|
20% |
100% |
(a)
Amount that Jaslyn spent on the home theater systems
= 4(1 u + 320)
= 4 u + 1280
Amount that Jaslyn spent on the water heaters
= 5 x 1 u
= 5 u
Amount that Jaslyn spent on the home theater systems in percent
= 100% - 20%
= 80%
20% → 5 u
80% → 4 x 5 u = 20 u
20 u = 4 u + 1280
20 u - 4 u = 1280
16 u = 1280
1 u = 1280 ÷ 16 = 80
Cost of each home theater system
= 80 + 320
= $400
(b)
100% → 5 u + 20 u = 25 u
Amount that Jaslyn spent altogether
= 25 u
= 25 x 80
= $2000
Answer(s): (a) $400; (b) $2000
