Jade bought 3 home theater systems and 7 food processors. Each home theater system costs $318 more than each food processor. She spent 25% of her money on the food processors.
- How much did each home theater system cost?
- How much did she spend altogether?
| |
Home theater systems |
Food processors |
Total |
| Number |
3 |
7 |
|
| Value |
1 u + $318 |
1 u |
|
| Total value |
3 u + $954 |
7 u |
|
Comparing amounts
spent on home theater systems
and food processors |
75%
|
25% |
100% |
(a)
Amount that Jade spent on the home theater systems
= 3(1 u + 318)
= 3 u + 954
Amount that Jade spent on the food processors
= 7 x 1 u
= 7 u
Amount that Jade spent on the home theater systems in percent
= 100% - 25%
= 75%
25% → 7 u
75% → 3 x 7 u = 21 u
21 u = 3 u + 954
21 u - 3 u = 954
18 u = 954
1 u = 954 ÷ 18 = 53
Cost of each home theater system
= 53 + 318
= $371
(b)
100% → 7 u + 21 u = 28 u
Amount that Jade spent altogether
= 28 u
= 28 x 53
= $1484
Answer(s): (a) $371; (b) $1484
