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 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~ :)
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)
To solve this problem, let's break it down step by step:
Step 1:
Let's assume there are 'x' number of boys and 'y' number of girls in the hall.
Step 2:
According to the given information, 1/4 of the girls are swimmers. So, the number of girl swimmers can be calculated as 1/4 * y.
Step 3:
Similarly, 2/5 of the boys are swimmers. So, the number of boy swimmers can be calculated as 2/5 * x.
Step 4:
According to the problem statement, the total number of swimmers is 110. So the equation can be formed by adding the number of girl swimmers and boy swimmers:
1/4 * y + 2/5 * x = 110
Step 5:
We also know that there were 335 children in the hall, which means the total number of boys and girls together is x + y = 335.
Step 6:
Now we have two equations:
1/4 * y + 2/5 * x = 110
x + y = 335
We can solve these equations to find the values of x and y.
This is a system of equations. One way to solve them is by substitution or elimination method.
Using the substitution method:
Let's solve equation 2 and express x in terms of y:
x = 335 - y
Now we can substitute this expression in equation 1:
1/4 * y + 2/5 * (335 - y) = 110
Simplifying the equation:
1/4 * y + 2/5 * 335 - 2/5 * y = 110
1/4 * y - 2/5 * y = 110 - 2/5 * 335
(1/4 - 2/5) * y = 110 - (2/5 * 335)
(5/20 - 8/20) * y = 110 - (670/20)
-3/20 * y = -560/20
y = (-560/20) / (-3/20)
y = 560 / 3
y = 186.66 (approx.)
Since the number of children must be a whole number, we can round the number of girls to 187.
Step 7:
Now we can find the number of boys by substituting the value of y into equation 2:
x + 187 = 335
x = 335 - 187
x = 148
So, there are 148 boys in the hall.