At first, Sam had 12 candy canes and Howard had 5 times as many candy canes as Sam. After they each received an equal number of candy canes from their cousin, Howard had four times as many candy canes as Sam. How many candy canes did their cousin give to both of them altogether?
| |
Sam |
Howard |
Difference |
| Before |
1x3 =
3 u |
5x3 =
15 u |
4x3 =
12 u |
| Change |
+ 1 u |
+ 1 u |
|
| After |
1x4 =
4 u |
4x4 =
16 u |
3x4 =
12 u |
Since both received an equal number of candy canes, the difference in the number of candy canes remains unchanged. LCM of 4 and 3 is 12.
3 u = 12
1 u = 12 ÷ 3 = 4
Number of candy canes that each received
= 4 u - 3 u
= 1 u
Number of candy canes that both of them received altogether
= 2 x 1 u
= 2 u
= 2 x 4
= 8
Answer(s): 8
