Ivory and Abi have some cards. If Ivory gives 12 cards to Abi, Abi will have 5 times the number of cards as Ivory. If Abi gives 30 cards to Ivory, Ivory will have
23 as many cards as Abi. How many cards does Ivory have at first?
|
Case 1 |
Case 2 |
|
Ivory |
Abi |
Ivory |
Abi |
Before |
5 u + 12 |
25 u - 12 |
12 u - 30 |
18 u + 30 |
Change |
- 12 |
+ 12 |
+ 30 |
- 30 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 u |
The total number of cards in both cases remains unchanged. Make the total number of cards in both cases the same. LCM of 6 and 5 is 30.
Number of cards that Ivory had at first is the same in both cases.
12 u - 30 = 5 u + 12
12 u - 5 u = 12 + 30
7 u = 42
1 u = 6
Number of cards that Ivory had at first
= 5 u + 12
= 5 x 6 + 12
= 30 + 12
= 42
Answer(s): 42