18 of the guests at a concert hall were women. 90% of the remaining guests were men and the rest were children. The total number of women and children is 506 less than the number of men. After some men entered the concert hall, 80% of the guests that remained were men. How many men entered the concert hall?
Women |
Children |
Men |
Total |
1x10 |
7x10 |
8x10 |
|
1x7 |
9x7 |
|
10 |
7 |
63 |
80 |
|
Women and children |
Men |
Before |
17x1 = 17 u |
63x1 = 63 u |
Change |
|
+ 5 u |
After
|
1x17 = 17 u |
4x17 = 68 u |
90% =
90100 =
910 Children : Men = 1 : 9
The total number of children and men at first is repeated. Make the total number of children at first the same. LCM of 7 and 10 is 70.
80% =
80100 =
45 When some men entered, the total number of women and children remains unchanged. Make the total number of women and children the same. LCM of 17 and 1 is 17.
The total number of women and children is 506 less than the number of men.
Number of less women and children than the number of men at first
= 63 u - 17 u
= 46 u
46 u = 506
1 u = 506 ÷ 46 = 11
Number of men who entered the concert hall
= 68 u - 63 u
= 5 u
= 5 x 11
= 55
Answer(s): 55