Opal and Emma had $106. Emma had $34 more than Opal. Opal spent 2 times as much as Emma and was left with
25 as much as Emma. How much did Opal spend?
| |
Make p the same
(1)x5 = (3) |
Opal
(1) |
Emma
(2) |
Make p the same
(2)x2 = (4) |
Total
|
Comparing Opal
and Emma at first |
|
|
$34 more |
|
$106 |
| Before |
$180 |
$36 |
$70 |
$140 |
|
| Change |
- 10 u |
- 2 u |
- 1 u |
- 2 u |
|
| After |
10 p |
2 p |
5 p |
10 p |
|
Amount that Opal had at first
= (106 - 34) ÷ 2
= 72 ÷ 2
= $36
Amount that Emma had at first
= 36 + 34
= $70
36 - 2 u = 2 p --- (1)
70 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
180 - 10 u =
10 p --- (3)
(2)
x 2
140 - 2 u =
10 p --- (4)
(4) = (3)
140 - 2 u = 180 - 10 u
10 u - 2 u = 180 - 140
8 u = 40
1 u = 40 ÷ 8 = 5
Amount that Opal spent
= 2 u
= 2 x 5
= $10
Answer(s): $10
