John had 5 times as many cards as Rael at first. Then each of them bought an equal number of new cards. In the end, Rael had 8 cards and John had 4 times as many cards as Rael. How many cards did both of them buy altogether?
| |
John |
Rael |
Difference |
| Before |
5x3 =
15 u |
1x3 =
3 u |
4x3 =
12 u |
| Change |
+ ? |
+ ? |
|
| After |
4x4 =
16 u |
1x4 =
4 u |
3x4 =
12 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 3 is 12.
Number of cards that Rael had in the end = 4 u
4 u = 8
1 u = 8 ÷ 4 = 2
Number of cards that John bought
= 16 u - 15 u
= 1 u
Number of cards that both of them bought altogether
= 2 x 1 u
= 2 u
= 2 x 2
= 4
Answer(s): 4
