Esther bought 6 televisions and 9 juicers. Each television costs $280 more than each juicer. She spent 20% of her money on the juicers.
- How much did each television cost?
- How much did she spend altogether?
| |
Televisions |
Juicers |
Total |
| Number |
6 |
9 |
|
| Value |
1 u + $280 |
1 u |
|
| Total value |
6 u + $1680 |
9 u |
|
Comparing amounts
spent on televisions
and juicers |
80%
|
20% |
100% |
(a)
Amount that Esther spent on the televisions
= 6(1 u + 280)
= 6 u + 1680
Amount that Esther spent on the juicers
= 9 x 1 u
= 9 u
Amount that Esther spent on the televisions in percent
= 100% - 20%
= 80%
20% → 9 u
80% → 4 x 9 u = 36 u
36 u = 6 u + 1680
36 u - 6 u = 1680
30 u = 1680
1 u = 1680 ÷ 30 = 56
Cost of each television
= 56 + 280
= $336
(b)
100% → 9 u + 36 u = 45 u
Amount that Esther spent altogether
= 45 u
= 45 x 56
= $2520
Answer(s): (a) $336; (b) $2520
