35 of Olivia's money was equal to
12 of Nora's money at first. After Olivia spent $76 and Nora spent
35 of her money, Olivia had
12 as much money as Nora.
- How much money did Nora have at first?
- How much money did Nora have in the end?
| |
Olivia |
Nora |
Comparing Olivia
and Nora at first |
5x5 =
25 u |
6x5 =
30 u |
| Before |
|
5x6 =
30 u |
| Change |
- $76 |
- 3x6 =
- 18 u |
| After |
|
2x6 =
12 u |
Comparing Olivia
and Nora in the end |
1x6 =
6 u |
2x6 =
12 u |
35 Olivia's money =
12 Nora's money
Make numerators the same.
35 Olivia's money =
1x32x3 Nora's money
35 Olivia's money =
36 Nora's money
Olivia's money : Nora's money = 5 : 6
The amount that Nora had at first is repeated. Make the amount that Nora had at first the same. LCM of 6 and 5 is 30.
Amount that Olivia spent
= 25 u - 6 u
= 19 u
19 u = 76
1 u = 76 ÷ 19 = 4
(a)
Amount that Nora had at first
= 30 u
= 30 x 4
= $120
(b)
Amount that Nora had in the end
= 12 u
= 12 x 4
= $48
Answer(s): (a) $120; (b) $48
