At first, Pierre had 12 candy canes and Gabriel had 6 times as many candy canes as Pierre. After they each received an equal number of candy canes from their father, Gabriel had thrice as many candy canes as Pierre. How many candy canes did their father give to both of them altogether?
| |
Pierre |
Gabriel |
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 candy canes, the difference in the number of candy canes remains unchanged. LCM of 5 and 2 is 10.
2 u = 12
1 u = 12 ÷ 2 = 6
Number of candy canes that each received
= 5 u - 2 u
= 3 u
Number of candy canes that both of them received altogether
= 2 x 3 u
= 6 u
= 6 x 6
= 36
Answer(s): 36
