Liam had 5 times as many cards as Fred at first. Then each of them bought an equal number of new cards. In the end, Fred had 12 cards and Liam had 3 times as many cards as Fred. How many cards did both of them buy altogether?
| |
Liam |
Fred |
Difference |
| Before |
5x1 =
5 u |
1x1 =
1 u |
4x1 =
4 u |
| Change |
+ ? |
+ ? |
|
| After |
3x2 =
6 u |
1x2 =
2 u |
2x2 =
4 u |
The difference in the number of cards at first and in the end remains unchanged. Make the difference in the number of cards at first and in the end the same. LCM of 4 and 2 is 4.
Number of cards that Fred had in the end = 2 u
2 u = 12
1 u = 12 ÷ 2 = 6
Number of cards that Liam bought
= 6 u - 5 u
= 1 u
Number of cards that both of them bought altogether
= 2 x 1 u
= 2 u
= 2 x 6
= 12
Answer(s): 12
