Jade and Jean have some marbles. If Jade gives 39 marbles to Jean, Jean will have 4 times the number of marbles as Jade. If Jean gives 45 marbles to Jade, Jade will have
35 as many marbles as Jean. How many marbles does Jade have at first?
| |
Case 1 |
Case 2 |
| |
Jade |
Jean |
Jade |
Jean |
| Before |
8 u + 39 |
32 u - 39 |
15 u - 45 |
25 u + 45 |
| Change |
- 39 |
+ 39 |
+ 45 |
- 45 |
| After |
1x8 =
8 u |
4x8 =
32 u |
3x5 =
15 u |
5x5 =
25 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 5 and 8 is 40.
Number of marbles that Jade had at first is the same in both cases.
15 u - 45 = 8 u + 39
15 u - 8 u = 39 + 45
7 u = 84
1 u = 12
Number of marbles that Jade had at first
= 8 u + 39
= 8 x 12 + 39
= 96 + 39
= 135
Answer(s): 135
