At first, Ivan had thrice as many mochi balls as John. After they each gave away 18 mochi balls, Ivan had 7 times as many mochi balls as John. How many mochi balls did they have altogether at first?
| |
Ivan |
John |
Difference |
| Before |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
| Change |
- 18 |
- 18 |
|
| After |
7 u |
1 u |
6 u |
Since they both gave away the same number of mochi balls, their difference in the number of mochi balls remains the same. Make the difference in the number of mochi balls the same. LCM of 2 and 6 is 6.
Number of mochi balls that each gave away
= 9 u - 7 u
= 2 u
2 u = 18
1 u = 18 ÷ 2 = 9
Number of mochi balls that they had altogether at first
= 9 u + 3 u
= 12 u
= 12 x 9
= 108
Answer(s): 108
