At first, Daniel had 18 candy canes and Archie had 5 times as many candy canes as Daniel. After they each received an equal number of candy canes from their niece, Archie had four times as many candy canes as Daniel. How many candy canes did their niece give to both of them altogether?
| |
Daniel |
Archie |
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 = 18
1 u = 18 ÷ 3 = 6
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 6
= 12
Answer(s): 12
