13 of Olivia's money was equal to
12 of Sarah's money at first. After Olivia spent $26 and Sarah spent
35 of her money, Olivia had
12 as much money as Sarah.
- How much money did Sarah have at first?
- How much money did Sarah have in the end?
| |
Olivia |
Sarah |
Comparing Olivia
and Sarah at first |
3x5 =
15 u |
2x5 =
10 u |
| Before |
|
5x2 =
10 u |
| Change |
- $26 |
- 3x2 =
- 6 u |
| After |
|
2x2 =
4 u |
Comparing Olivia
and Sarah in the end |
1x2 =
2 u |
2x2 =
4 u |
13 Olivia's money =
12 Sarah's money
Make numerators the same.
13 Olivia's money =
1x12x1 Sarah's money
13 Olivia's money =
12 Sarah's money
Olivia's money : Sarah's money = 3 : 2
The amount that Sarah had at first is repeated. Make the amount that Sarah had at first the same. LCM of 2 and 5 is 10.
Amount that Olivia spent
= 15 u - 2 u
= 13 u
13 u = 26
1 u = 26 ÷ 13 = 2
(a)
Amount that Sarah had at first
= 10 u
= 10 x 2
= $20
(b)
Amount that Sarah had in the end
= 4 u
= 4 x 2
= $8
Answer(s): (a) $20; (b) $8
