At first, Carl had twice as many mochi balls as Archie. After they each gave away 12 mochi balls, Carl had 6 times as many mochi balls as Archie. How many mochi balls did they have altogether at first?
| |
Carl |
Archie |
Difference |
| Before |
2x5 =
10 u |
1x5 =
5 u |
1x5 =
5 u |
| Change |
- 12 |
- 12 |
|
| After |
6 u |
1 u |
5 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 1 and 5 is 5.
Number of mochi balls that each gave away
= 10 u - 6 u
= 4 u
4 u = 12
1 u = 12 ÷ 4 = 3
Number of mochi balls that they had altogether at first
= 10 u + 5 u
= 15 u
= 15 x 3
= 45
Answer(s): 45
