35 of Emma's money was equal to
13 of Diana's money at first. After Emma spent $112 and Diana spent
35 of her money, Emma had
12 as much money as Diana.
- How much money did Diana have at first?
- How much money did Diana have in the end?
| |
Emma |
Diana |
Comparing Emma
and Diana at first |
5x5 =
25 u |
9x5 =
45 u |
| Before |
|
5x9 =
45 u |
| Change |
- $112 |
- 3x9 =
- 27 u |
| After |
|
2x9 =
18 u |
Comparing Emma
and Diana in the end |
1x9 =
9 u |
2x9 =
18 u |
35 Emma's money =
13 Diana's money
Make numerators the same.
35 Emma's money =
1x33x3 Diana's money
35 Emma's money =
39 Diana's money
Emma's money : Diana's money = 5 : 9
The amount that Diana had at first is repeated. Make the amount that Diana had at first the same. LCM of 9 and 5 is 45.
Amount that Emma spent
= 25 u - 9 u
= 16 u
16 u = 112
1 u = 112 ÷ 16 = 7
(a)
Amount that Diana had at first
= 45 u
= 45 x 7
= $315
(b)
Amount that Diana had in the end
= 18 u
= 18 x 7
= $126
Answer(s): (a) $315; (b) $126
