At first, Xavier had 22 lollipops and Ken had 6 times as many lollipops as Xavier. After they each received an equal number of lollipops from their mother, Ken had thrice as many lollipops as Xavier. How many lollipops did their mother give to both of them altogether?
| |
Xavier |
Ken |
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 lollipops, the difference in the number of lollipops remains unchanged. LCM of 5 and 2 is 10.
2 u = 22
1 u = 22 ÷ 2 = 11
Number of lollipops that each received
= 5 u - 2 u
= 3 u
Number of lollipops that both of them received altogether
= 2 x 3 u
= 6 u
= 6 x 11
= 66
Answer(s): 66
