Cody and Tom shared some cards in the ratio of 3 : 7. After both each gave away 45 cards to their sister, the ratio of the number of cards Cody had to the total number of cards left was 1 : 5. How many cards did the two boys have at first?
| |
Cody |
Tom |
Difference |
| Before |
3x3 =
9 u |
7x3 =
21 u |
4x3 =
12 u |
| Change |
- 45 |
- 45 |
|
| After |
1x4 =
4 u |
4x4 =
16 u |
3x4 =
12 u |
Number of cards that Cody and Tom each gave to their sister is the same.
The difference in the number of cards at first and in the end between Cody and Tom remains unchanged. Make the difference in the number of cards the same. LCM of 4 and 3 is 12.
Number of cards that Cody gave to their sister
= 9 u - 4 u
= 5 u
5 u = 45
1 u = 45 ÷ 5 = 9
Number of cards that the two boys had at first
= 9 u + 21 u
= 30 u
= 30 x 9
= 270
Answer(s): 270
