35 of Cathy's money was equal to
13 of Erika's money at first. After Cathy spent $14 and Erika spent
13 of her money, Cathy had
12 as much money as Erika.
- How much money did Erika have at first?
- How much money did Erika have in the end?
| |
Cathy |
Erika |
Comparing Cathy
and Erika at first |
5x1 =
5 u |
9x1 =
9 u |
| Before |
|
3x3 =
9 u |
| Change |
- $14 |
- 1x3 =
- 3 u |
| After |
|
2x3 =
6 u |
Comparing Cathy
and Erika in the end |
1x3 =
3 u |
2x3 =
6 u |
35 Cathy's money =
13 Erika's money
Make numerators the same.
35 Cathy's money =
1x33x3 Erika's money
35 Cathy's money =
39 Erika's money
Cathy's money : Erika's money = 5 : 9
The amount that Erika had at first is repeated. Make the amount that Erika had at first the same. LCM of 9 and 3 is 9.
Amount that Cathy spent
= 5 u - 3 u
= 2 u
2 u = 14
1 u = 14 ÷ 2 = 7
(a)
Amount that Erika had at first
= 9 u
= 9 x 7
= $63
(b)
Amount that Erika had in the end
= 6 u
= 6 x 7
= $42
Answer(s): (a) $63; (b) $42
