34 of Gwen's money was equal to
13 of Anna's money at first. After Gwen spent $33 and Anna spent
35 of her money, Gwen had
12 as much money as Anna.
- How much money did Anna have at first?
- How much money did Anna have in the end?
| |
Gwen |
Anna |
Comparing Gwen
and Anna at first |
4x5 =
20 u |
9x5 =
45 u |
| Before |
|
5x9 =
45 u |
| Change |
- $33 |
- 3x9 =
- 27 u |
| After |
|
2x9 =
18 u |
Comparing Gwen
and Anna in the end |
1x9 =
9 u |
2x9 =
18 u |
34 Gwen's money =
13 Anna's money
Make numerators the same.
34 Gwen's money =
1x33x3 Anna's money
34 Gwen's money =
39 Anna's money
Gwen's money : Anna's money = 4 : 9
The amount that Anna had at first is repeated. Make the amount that Anna had at first the same. LCM of 9 and 5 is 45.
Amount that Gwen spent
= 20 u - 9 u
= 11 u
11 u = 33
1 u = 33 ÷ 11 = 3
(a)
Amount that Anna had at first
= 45 u
= 45 x 3
= $135
(b)
Amount that Anna had in the end
= 18 u
= 18 x 3
= $54
Answer(s): (a) $135; (b) $54
