At first, Ryan had 30 candy canes and Zeph had 6 times as many candy canes as Ryan. After they each received an equal number of candy canes from their neighbour, Zeph had thrice as many candy canes as Ryan. How many candy canes did their neighbour give to both of them altogether?
| |
Ryan |
Zeph |
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 = 30
1 u = 30 ÷ 2 = 15
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 15
= 90
Answer(s): 90
