At first, Harry had 22 mochi balls and Owen had 6 times as many mochi balls as Harry. After they each received an equal number of mochi balls from their cousin, Owen had thrice as many mochi balls as Harry. How many mochi balls did their cousin give to both of them altogether?
| |
Harry |
Owen |
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
