At first, Ben had 22 lollipops and Ethan had 6 times as many lollipops as Ben. After they each received an equal number of lollipops from their father, Ethan had thrice as many lollipops as Ben. How many lollipops did their father give to both of them altogether?
| |
Ben |
Ethan |
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
