There were some boys and girls in the school hall at first. 40% of the boys and 10% of the girls left the school hall. As a result, 3/4 of the pupils remained in the school hall.There were 12 more girls than boys who remained in the school hall. how many boys were there at first?
If there were originally b boys and g girls,
.60b + .90g = .75(b+g)
.9g = .6b+12
solve for b
It's a bit less cumbersome if you get rid of those pesky decimals
60b+90g = 75b+75g
3g = 2b+40
60b + 30(2b+40) = 75b+25(2b+40)
b = 40
To find the number of boys initially, we need to follow a step-by-step approach:
Step 1: Let's assume the initial number of boys to be x.
Step 2: As mentioned, 40% of boys left, which means (40/100)x boys left the school hall.
Step 3: Similarly, let's assume the initial number of girls to be y.
Step 4: As mentioned, 10% of girls left, which means (10/100)y girls left the school hall.
Step 5: After the above departures, the remaining number of boys in the school hall is x - (40/100)x, which simplifies to (60/100)x.
Step 6: And the remaining number of girls in the school hall is y - (10/100)y, which simplifies to (90/100)y.
Step 7: According to the given information, 3/4 of the pupils remained in the school hall. This means that (3/4) of the total students (boys + girls) stayed.
Step 8: The total number of students initially was x (boys) + y (girls).
Step 9: From Step 7, we can write the equation: (3/4) * (x + y) = (60/100)x + (90/100)y.
Step 10: According to the given information, there were 12 more girls than boys remaining in the school hall: (90/100)y = (60/100)x + 12.
Step 11: Now we have a system of two equations:
- First equation: (3/4) * (x + y) = (60/100)x + (90/100)y.
- Second equation: (90/100)y = (60/100)x + 12.
Step 12: Solve this system of equations to find the values of x and y.
By solving the above system of equations, we can find the initial number of boys (x).