At first, Xavier had 10 candy canes and Eric had 6 times as many candy canes as Xavier. After they each received an equal number of candy canes from their friend, Eric had thrice as many candy canes as Xavier. How many candy canes did their friend give to both of them altogether?
| |
Xavier |
Eric |
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 = 10
1 u = 10 ÷ 2 = 5
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 5
= 30
Answer(s): 30
