maths
posted by mathsmad on .
There were 335 children in a hall. 1/4 of the girls and 2/5 of the boys are swimmers. There are 110 swimmers in all. How many boys are there in the hall?

first we represent unknowns using variables.
let x = number of girls in the hall
since the the total number of children is 335,
let 335  x = number of boys in the hall
then we setup the equation. since 1/4 of the girls and 2/5 of the boys are swimmers and their total is 110,
(1/4)*x + (2/5)*(335  x) = 110
(1/4)*x + 134  (2/5)*x = 110
(1/4  2/5)*x = 110  134
(5/20  8/20)*x = 24
(3/20)*x = 24
to get x alone, we multiply both sides by the reciprocal of the numerical coefficient (the number before the variable). thus:
[(3/20)*x = 24]*(20/3)
x = 160 (number of girls)
335x = 175 (number of boys)
hope this helps~ :) 
could you pls show me a non algebra way as i have not learnt algebra yet, tks

1/4 girl + 2/5 boy = 110
3/4 girl + 3/5 boy = 335 110 =225
3/4 girl + 6/5 boy = 110 X 3 = 330
3/5 boy = 330  225 = 105
1/5boy = 105/3 = 35
5/5 boy = 35 X 5 = 175 (answer)