Diana and Jade have some marbles. If Diana gives 25 marbles to Jade, Jade will have 5 times the number of marbles as Diana. If Jade gives 35 marbles to Diana, Diana will have
25 as many marbles as Jade. How many marbles does Diana have at first?
|
Case 1 |
Case 2 |
|
Diana |
Jade |
Diana |
Jade |
Before |
7 u + 25 |
35 u - 25 |
12 u - 35 |
30 u + 35 |
Change |
- 25 |
+ 25 |
+ 35 |
- 35 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 6 and 7 is 42.
Number of marbles that Diana had at first is the same in both cases.
12 u - 35 = 7 u + 25
12 u - 7 u = 25 + 35
5 u = 60
1 u = 12
Number of marbles that Diana had at first
= 7 u + 25
= 7 x 12 + 25
= 84 + 25
= 109
Answer(s): 109