18 of the visitors at a zoo were men. 70% of the remaining visitors were women and the rest were children. The total number of men and children is 108 less than the number of women. After some women entered the zoo, 75% of the visitors that remained were women. How many women entered the zoo?
Men |
Children |
Women |
Total |
1x10 |
7x10 |
8x10 |
|
3x7 |
7x7 |
|
10 |
21 |
49 |
80 |
|
Men and children |
Women |
Before |
31x1 = 31 u |
49x1 = 49 u |
Change |
|
+ 44 u |
After
|
1x31 = 31 u |
3x31 = 93 u |
70% =
70100 =
710 Children : Women = 3 : 7
The total number of children and women at first is repeated. Make the total number of children at first the same. LCM of 7 and 10 is 70.
75% =
75100 =
34 When some women entered, the total number of men and children remains unchanged. Make the total number of men and children the same. LCM of 31 and 1 is 31.
The total number of men and children is 108 less than the number of women.
Number of less men and children than the number of women at first
= 49 u - 31 u
= 18 u
18 u = 108
1 u = 108 ÷ 18 = 6
Number of women who entered the zoo
= 93 u - 49 u
= 44 u
= 44 x 6
= 264
Answer(s): 264