Question

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?

Answer 1

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 set-up 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)
335-x = 175 (number of boys)

hope this helps~ :)

Answer 2

could you pls show me a non- algebra way as i have not learnt algebra yet, tks

Answer 3

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)