Natalie and Zara have some coins. If Natalie gives 30 coins to Zara, Zara will have 5 times the number of coins as Natalie. If Zara gives 50 coins to Natalie, Natalie will have
25 as many coins as Zara. How many coins does Natalie have at first?
|
Case 1 |
Case 2 |
|
Natalie |
Zara |
Natalie |
Zara |
Before |
7 u + 30 |
35 u - 30 |
12 u - 50 |
30 u + 50 |
Change |
- 30 |
+ 30 |
+ 50 |
- 50 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 6 and 7 is 42.
Number of coins that Natalie had at first is the same in both cases.
12 u - 50 = 7 u + 30
12 u - 7 u = 30 + 50
5 u = 80
1 u = 16
Number of coins that Natalie had at first
= 7 u + 30
= 7 x 16 + 30
= 112 + 30
= 142
Answer(s): 142