23 of Barbara's money was equal to
12 of Olivia's money at first. After Barbara spent $20 and Olivia spent
13 of her money, Barbara had
12 as much money as Olivia.
- How much money did Olivia have at first?
- How much money did Olivia have in the end?
| |
Barbara |
Olivia |
Comparing Barbara
and Olivia at first |
3x3 =
9 u |
4x3 =
12 u |
| Before |
|
3x4 =
12 u |
| Change |
- $20 |
- 1x4 =
- 4 u |
| After |
|
2x4 =
8 u |
Comparing Barbara
and Olivia in the end |
1x4 =
4 u |
2x4 =
8 u |
23 Barbara's money =
12 Olivia's money
Make numerators the same.
23 Barbara's money =
1x22x2 Olivia's money
23 Barbara's money =
24 Olivia's money
Barbara's money : Olivia's money = 3 : 4
The amount that Olivia had at first is repeated. Make the amount that Olivia had at first the same. LCM of 4 and 3 is 12.
Amount that Barbara spent
= 9 u - 4 u
= 5 u
5 u = 20
1 u = 20 ÷ 5 = 4
(a)
Amount that Olivia had at first
= 12 u
= 12 x 4
= $48
(b)
Amount that Olivia had in the end
= 8 u
= 8 x 4
= $32
Answer(s): (a) $48; (b) $32
