Xylia bought 3 portable air-conditioners and 8 speakers. Each portable air-conditioner costs $460 more than each speaker. She spent 10% of her money on the speakers.
- How much did each portable air-conditioner cost?
- How much did she spend altogether?
| |
Portable air-conditioners |
Speakers |
Total |
| Number |
3 |
8 |
|
| Value |
1 u + $460 |
1 u |
|
| Total value |
3 u + $1380 |
8 u |
|
Comparing amounts
spent on portable air-conditioners
and speakers |
90%
|
10% |
100% |
(a)
Amount that Xylia spent on the portable air-conditioners
= 3(1 u + 460)
= 3 u + 1380
Amount that Xylia spent on the speakers
= 8 x 1 u
= 8 u
Amount that Xylia spent on the portable air-conditioners in percent
= 100% - 10%
= 90%
10% → 8 u
90% → 9 x 8 u = 72 u
72 u = 3 u + 1380
72 u - 3 u = 1380
69 u = 1380
1 u = 1380 ÷ 69 = 20
Cost of each portable air-conditioner
= 20 + 460
= $480
(b)
100% → 8 u + 72 u = 80 u
Amount that Xylia spent altogether
= 80 u
= 80 x 20
= $1600
Answer(s): (a) $480; (b) $1600
