45 of Shiyun's money was equal to
13 of Betty's money at first. After Shiyun spent $130 and Betty spent
35 of her money, Shiyun had
12 as much money as Betty.
- How much money did Betty have at first?
- How much money did Betty have in the end?
| |
Shiyun |
Betty |
Comparing Shiyun
and Betty at first |
5x5 =
25 u |
12x5 =
60 u |
| Before |
|
5x12 =
60 u |
| Change |
- $130 |
- 3x12 =
- 36 u |
| After |
|
2x12 =
24 u |
Comparing Shiyun
and Betty in the end |
1x12 =
12 u |
2x12 =
24 u |
45 Shiyun's money =
13 Betty's money
Make numerators the same.
45 Shiyun's money =
1x43x4 Betty's money
45 Shiyun's money =
412 Betty's money
Shiyun's money : Betty's money = 5 : 12
The amount that Betty had at first is repeated. Make the amount that Betty had at first the same. LCM of 12 and 5 is 60.
Amount that Shiyun spent
= 25 u - 12 u
= 13 u
13 u = 130
1 u = 130 ÷ 13 = 10
(a)
Amount that Betty had at first
= 60 u
= 60 x 10
= $600
(b)
Amount that Betty had in the end
= 24 u
= 24 x 10
= $240
Answer(s): (a) $600; (b) $240
