Paul, Gabriel and Carl shared $123. During a shopping trip, Paul spent
25 of his share, Gabriel spent
34 of his share and Carl spent
13 of his share. Given that all three boys each spent the same amount of money, how much more money do Paul and Gabriel have than Carl at first?
| |
Paul |
Gabriel |
Carl |
Total |
| Before |
5x3 =
15 u |
4x2 =
8 u |
3x6 =
18 u |
$123 |
| Change |
- 2x3 =
- 6 u |
- 3x2 =
- 6 u |
- 1x6 =
- 6 u |
|
| After |
3x3 =
9 u |
1x2 =
2 u |
2x6 =
12 u |
|
The amounts that Paul, Gabriel and Carl spent is the same. Make the amounts that each boy spent the same. LCM of 2, 3 and 1 is 6.
Amounts that the 3 boys had at first
= 15 u + 8 u + 18 u
= 41 u
41 u = 123
1 u = 123 ÷ 41 = 3
Amount that Paul and Gabriel have at first
= 15 u + 8 u
= 23 u
Amount that Paul and Gabriel have more than Carl at first
= 23 u - 18 u
= 5 u
= 5 x 3
= $15
Answer(s): $15
