At first, Liam had thrice as many candy canes as Ken. After they each gave away 12 candy canes, Liam had 7 times as many candy canes as Ken. How many candy canes did they have altogether at first?
| |
Liam |
Ken |
Difference |
| Before |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
| Change |
- 12 |
- 12 |
|
| After |
7 u |
1 u |
6 u |
Since they both gave away the same number of candy canes, their difference in the number of candy canes remains the same. Make the difference in the number of candy canes the same. LCM of 2 and 6 is 6.
Number of candy canes that each gave away
= 9 u - 7 u
= 2 u
2 u = 12
1 u = 12 ÷ 2 = 6
Number of candy canes that they had altogether at first
= 9 u + 3 u
= 12 u
= 12 x 6
= 72
Answer(s): 72
