Zeph and Daniel shared some cards in the ratio of 4 : 7. After both each gave away 40 cards to their brother, the ratio of the number of cards Zeph had to the total number of cards left was 1 : 4. How many cards did the two boys have at first?
|
Zeph |
Daniel |
Difference |
Before |
4x2 = 8 u |
7x2 = 14 u |
3x2 = 6 u |
Change |
- 40 |
- 40 |
|
After |
1x3 = 3 u |
3x3 = 9 u |
2x3 = 6 u |
Number of cards that Zeph and Daniel each gave to their brother is the same.
The difference in the number of cards at first and in the end between Zeph and Daniel remains unchanged. Make the difference in the number of cards the same. LCM of 3 and 2 is 6.
Number of cards that Zeph gave to their brother
= 8 u - 3 u
= 5 u
5 u = 40
1 u = 40 ÷ 5 = 8
Number of cards that the two boys had at first
= 8 u + 14 u
= 22 u
= 22 x 8
= 176
Answer(s): 176