At first, Archie had 27 mini cupcakes and Sam had 6 times as many mini cupcakes as Archie. After they each received an equal number of mini cupcakes from their father, Sam had four times as many mini cupcakes as Archie. How many mini cupcakes did their father give to both of them altogether?
| |
Archie |
Sam |
Difference |
| Before |
1x3 =
3 u |
6x3 =
18 u |
5x3 =
15 u |
| Change |
+ 2 u |
+ 2 u |
|
| After |
1x5 =
5 u |
4x5 =
20 u |
3x5 =
15 u |
Since both received an equal number of mini cupcakes, the difference in the number of mini cupcakes remains unchanged. LCM of 5 and 3 is 15.
3 u = 27
1 u = 27 ÷ 3 = 9
Number of mini cupcakes that each received
= 5 u - 3 u
= 2 u
Number of mini cupcakes that both of them received altogether
= 2 x 2 u
= 4 u
= 4 x 9
= 36
Answer(s): 36
