At first, Paul had 30 mini cupcakes and Carl had 6 times as many mini cupcakes as Paul. After they each received an equal number of mini cupcakes from their father, Carl had thrice as many mini cupcakes as Paul. How many mini cupcakes did their father give to both of them altogether?
| |
Paul |
Carl |
Difference |
| Before |
1x2 =
2 u |
6x2 =
12 u |
5x2 =
10 u |
| Change |
+ 3 u |
+ 3 u |
|
| After |
1x5 =
5 u |
3x5 =
15 u |
2x5 =
10 u |
Since both received an equal number of mini cupcakes, the difference in the number of mini cupcakes remains unchanged. LCM of 5 and 2 is 10.
2 u = 30
1 u = 30 ÷ 2 = 15
Number of mini cupcakes that each received
= 5 u - 2 u
= 3 u
Number of mini cupcakes that both of them received altogether
= 2 x 3 u
= 6 u
= 6 x 15
= 90
Answer(s): 90
