At first, Sam had 12 mochi balls and Fred had 5 times as many mochi balls as Sam. After they each received an equal number of mochi balls from their cousin, Fred had four times as many mochi balls as Sam. How many mochi balls did their cousin give to both of them altogether?
| |
Sam |
Fred |
Difference |
| Before |
1x3 =
3 u |
5x3 =
15 u |
4x3 =
12 u |
| Change |
+ 1 u |
+ 1 u |
|
| After |
1x4 =
4 u |
4x4 =
16 u |
3x4 =
12 u |
Since both received an equal number of mochi balls, the difference in the number of mochi balls remains unchanged. LCM of 4 and 3 is 12.
3 u = 12
1 u = 12 ÷ 3 = 4
Number of mochi balls that each received
= 4 u - 3 u
= 1 u
Number of mochi balls that both of them received altogether
= 2 x 1 u
= 2 u
= 2 x 4
= 8
Answer(s): 8
