13 of Gem's money was equal to
14 of Xylia's money at first. After Gem spent $45 and Xylia spent
13 of her money, Gem had
12 as much money as Xylia.
- How much money did Xylia have at first?
- How much money did Xylia have in the end?
| |
Gem |
Xylia |
Comparing Gem
and Xylia at first |
3x3 =
9 u |
4x3 =
12 u |
| Before |
|
3x4 =
12 u |
| Change |
- $45 |
- 1x4 =
- 4 u |
| After |
|
2x4 =
8 u |
Comparing Gem
and Xylia in the end |
1x4 =
4 u |
2x4 =
8 u |
13 Gem's money =
14 Xylia's money
Make numerators the same.
13 Gem's money =
1x14x1 Xylia's money
13 Gem's money =
14 Xylia's money
Gem's money : Xylia's money = 3 : 4
The amount that Xylia had at first is repeated. Make the amount that Xylia had at first the same. LCM of 4 and 3 is 12.
Amount that Gem spent
= 9 u - 4 u
= 5 u
5 u = 45
1 u = 45 ÷ 5 = 9
(a)
Amount that Xylia had at first
= 12 u
= 12 x 9
= $108
(b)
Amount that Xylia had in the end
= 8 u
= 8 x 9
= $72
Answer(s): (a) $108; (b) $72
