Fiona bought 3 portable air-conditioners and 7 speakers. Each portable air-conditioner costs $440 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 |
7 |
|
Value |
1 u + $440 |
1 u |
|
Total value |
3 u + $1320 |
7 u |
|
Comparing amounts spent on portable air-conditioners and speakers |
90%
|
10% |
100% |
(a)
Amount that Fiona spent on the portable air-conditioners
= 3(1 u + 440)
= 3 u + 1320
Amount that Fiona spent on the speakers
= 7 x 1 u
= 7 u
Amount that Fiona spent on the portable air-conditioners in percent
= 100% - 10%
= 90%
10% → 7 u
90% → 9 x 7 u = 63 u
63 u = 3 u + 1320
63 u - 3 u = 1320
60 u = 1320
1 u = 1320 ÷ 60 = 22
Cost of each portable air-conditioner
= 22 + 440
= $462
(b)
100% → 7 u + 63 u = 70 u
Amount that Fiona spent altogether
= 70 u
= 70 x 22
= $1540
Answer(s): (a) $462; (b) $1540