Usha and Rachel had $124. Rachel had $8 more than Usha. Usha spent 3 times as much as Rachel and was left with
23 as much as Rachel. How much did Usha spend more than Rachel?
| |
Make p the same
(1)x3 = (3) |
Usha
(1) |
Rachel
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Usha
and Rachel at first |
|
|
$8 more |
|
$124 |
| Before |
$174 |
$58 |
$66 |
$132 |
|
| Change |
- 9 u |
- 3 u |
- 1 u |
- 2 u |
|
| After |
6 p |
2 p |
3 p |
6 p |
|
Amount that Usha had at first
= (124 - 8) ÷ 2
= 116 ÷ 2
= $58
Amount that Rachel had at first
= 58 + 8
= $66
58 - 3 u = 2 p --- (1)
66 - 1 u = 3 p --- (2)
Make p the same.
(1)
x 3
174 - 9 u =
6 p --- (3)
(2)
x 2
132 - 2 u =
6 p --- (4)
(4) = (3)
132 - 2 u = 174 - 9 u
9 u - 2 u = 174 - 132
7 u = 42
1 u = 42 ÷ 7 = 6
Amount that Usha spent more than Rachel
= 3 u - 1 u
= 2 u
= 2 x 6
= $12
Answer(s): $12
