Olivia bought 8 dishwashers and 10 stand mixers. Each dishwasher costs $448 more than each stand mixer. She spent 20% of her money on the stand mixers.
- How much did each dishwasher cost?
- How much did she spend altogether?
| |
Dishwashers |
Stand mixers |
Total |
| Number |
8 |
10 |
|
| Value |
1 u + $448 |
1 u |
|
| Total value |
8 u + $3584 |
10 u |
|
Comparing amounts
spent on dishwashers
and stand mixers |
80%
|
20% |
100% |
(a)
Amount that Olivia spent on the dishwashers
= 8(1 u + 448)
= 8 u + 3584
Amount that Olivia spent on the stand mixers
= 10 x 1 u
= 10 u
Amount that Olivia spent on the dishwashers in percent
= 100% - 20%
= 80%
20% → 10 u
80% → 4 x 10 u = 40 u
40 u = 8 u + 3584
40 u - 8 u = 3584
32 u = 3584
1 u = 3584 ÷ 32 = 112
Cost of each dishwasher
= 112 + 448
= $560
(b)
100% → 10 u + 40 u = 50 u
Amount that Olivia spent altogether
= 50 u
= 50 x 112
= $5600
Answer(s): (a) $560; (b) $5600
