SOLUTION: Please Help!!! Q) In a school 5/2 times the square root of the total number of children play football, one fourth of the total number of children play tennis and the remaining 28 c

Algebra ->  Equations -> SOLUTION: Please Help!!! Q) In a school 5/2 times the square root of the total number of children play football, one fourth of the total number of children play tennis and the remaining 28 c      Log On


   

Question 925610: Please Help!!! Q) In a school 5/2 times the square root of the total number of children play football, one fourth of the total number of children play tennis and the remaining 28 children play basketball. Find the total number of children in school??
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if the total number of children is x
%285%2F2%29sqrt%28x%29 play football
%281%2F4%29x play tennis
the remaining 28 children play basketball
so, x=%285%2F2%29sqrt%28x%29%2B%281%2F4%29x%2B28 ....solve for x, both sides multiply by 4
4x=4%285%2F2%29sqrt%28x%29%2B4%281%2F4%29x%2B28%2A4
4x=10sqrt%28x%29%2Bx%2B112
3x-112=10sqrt%28x%29....square both sides
%283x-112%29%5E2=%2810sqrt%28x%29%29%5E2
9x%5E2-672x%2B12544=100x
9x%5E2-672x-100x%2B12544=0
9x%5E2-772x%2B12544=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-772%29+%2B-+sqrt%28+%28-772%29%5E2-4%2A9%2A12544+%29%29%2F%282%2A9%29+

x+=+%28772+%2B-+sqrt%28+595984-451584+%29%29%2F18+

x+=+%28772+%2B-+sqrt%28+144400+%29%29%2F18+

x+=+%28772+%2B-+380%29%2F18+
solutions:
x+=+%28772+%2B380%29%2F18+
x+=+1152%2F18+
x+=+64
or
x+=+%28772+-380%29%2F18+
x+=+392%2F18+
x+=+21.78+ ...we can not use decimal for number of the children

=> our solution is highlight%28x+=+64+%29
check:
so, if the total number of children is 64
%285%2F2%29sqrt%2864%29=%285%2F2%29%2A8=5%2A4=20 play football
%281%2F4%2964=64%2F4=16 play tennis
the remaining 64-%2820%2B16%29=64-36=28 children play basketball