Hilda bought 3 home theater systems and 10 slow cookers. Each home theater system costs $252 more than each slow cooker. She spent 25% of her money on the slow cookers.
- How much did each home theater system cost?
- How much did she spend altogether?
|
Home theater systems |
Slow cookers |
Total |
Number |
3 |
10 |
|
Value |
1 u + $252 |
1 u |
|
Total value |
3 u + $756 |
10 u |
|
Comparing amounts spent on home theater systems and slow cookers |
75%
|
25% |
100% |
(a)
Amount that Hilda spent on the home theater systems
= 3(1 u + 252)
= 3 u + 756
Amount that Hilda spent on the slow cookers
= 10 x 1 u
= 10 u
Amount that Hilda spent on the home theater systems in percent
= 100% - 25%
= 75%
25% → 10 u
75% → 3 x 10 u = 30 u
30 u = 3 u + 756
30 u - 3 u = 756
27 u = 756
1 u = 756 ÷ 27 = 28
Cost of each home theater system
= 28 + 252
= $280
(b)
100% → 10 u + 30 u = 40 u
Amount that Hilda spent altogether
= 40 u
= 40 x 28
= $1120
Answer(s): (a) $280; (b) $1120