Jen and Emma have some marbles. If Jen gives 16 marbles to Emma, Emma will have 4 times the number of marbles as Jen. If Emma gives 23 marbles to Jen, Jen will have
25 as many marbles as Emma. How many marbles does Jen have at first?
|
Case 1 |
Case 2 |
|
Jen |
Emma |
Jen |
Emma |
Before |
7 u + 16 |
28 u - 16 |
10 u - 23 |
25 u + 23 |
Change |
- 16 |
+ 16 |
+ 23 |
- 23 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 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 7 is 35.
Number of marbles that Jen had at first is the same in both cases.
10 u - 23 = 7 u + 16
10 u - 7 u = 16 + 23
3 u = 39
1 u = 13
Number of marbles that Jen had at first
= 7 u + 16
= 7 x 13 + 16
= 91 + 16
= 107
Answer(s): 107