At first, Ken had 14 mochi balls and Henry had 6 times as many mochi balls as Ken. After they each received an equal number of mochi balls from their best friend, Henry had thrice as many mochi balls as Ken. How many mochi balls did their best friend give to both of them altogether?
| |
Ken |
Henry |
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 = 14
1 u = 14 ÷ 2 = 7
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 7
= 42
Answer(s): 42
