Emma and Pamela had $164. Pamela had $48 more than Emma. Emma spent 3 times as much as Pamela and was left with
25 as much as Pamela. How much did Emma spend?
| |
Make p the same
(1)x5 = (3) |
Emma
(1) |
Pamela
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Emma
and Pamela at first |
|
|
$48 more |
|
$164 |
| Before |
$290 |
$58 |
$106 |
$212 |
|
| Change |
- 15 u |
- 3 u |
- 1 u |
- 2 u |
|
| After |
10 p |
2 p |
5 p |
10 p |
|
Amount that Emma had at first
= (164 - 48) ÷ 2
= 116 ÷ 2
= $58
Amount that Pamela had at first
= 58 + 48
= $106
58 - 3 u = 2 p --- (1)
106 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
290 - 15 u =
10 p --- (3)
(2)
x 2
212 - 2 u =
10 p --- (4)
(4) = (3)
212 - 2 u = 290 - 15 u
15 u - 2 u = 290 - 212
13 u = 78
1 u = 78 ÷ 13 = 6
Amount that Emma spent
= 3 u
= 3 x 6
= $18
Answer(s): $18
