At first, Ian had 22 mochi balls and Nick had 6 times as many mochi balls as Ian. After they each received an equal number of mochi balls from their friend, Nick had thrice as many mochi balls as Ian. How many mochi balls did their friend give to both of them altogether?
| |
Ian |
Nick |
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 mochi balls, the difference in the number of mochi balls remains unchanged. LCM of 5 and 2 is 10.
2 u = 22
1 u = 22 ÷ 2 = 11
Number of mochi balls that each received
= 5 u - 2 u
= 3 u
Number of mochi balls that both of them received altogether
= 2 x 3 u
= 6 u
= 6 x 11
= 66
Answer(s): 66
