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