35 of Gabby's money was equal to
13 of Betty's money at first. After Gabby spent $33 and Betty spent
14 of her money, Gabby had
13 as much money as Betty.
- How much money did Betty have at first?
- How much money did Betty have in the end?
| |
Gabby |
Betty |
Comparing Gabby
and Betty at first |
5x4 =
20 u |
9x4 =
36 u |
| Before |
|
4x9 =
36 u |
| Change |
- $33 |
- 1x9 =
- 9 u |
| After |
|
3x9 =
27 u |
Comparing Gabby
and Betty in the end |
1x9 =
9 u |
3x9 =
27 u |
35 Gabby's money =
13 Betty's money
Make numerators the same.
35 Gabby's money =
1x33x3 Betty's money
35 Gabby's money =
39 Betty's money
Gabby's money : Betty's money = 5 : 9
The amount that Betty had at first is repeated. Make the amount that Betty had at first the same. LCM of 9 and 4 is 36.
Amount that Gabby spent
= 20 u - 9 u
= 11 u
11 u = 33
1 u = 33 ÷ 11 = 3
(a)
Amount that Betty had at first
= 36 u
= 36 x 3
= $108
(b)
Amount that Betty had in the end
= 27 u
= 27 x 3
= $81
Answer(s): (a) $108; (b) $81
