3/4 of the number of girls in school is if to half to number of boys . If the school has 1420pupiles ,how many of them are boys?
pupils
If there are b boys, then we know that
3/4 (1420-b) = 1/2 b
b = 852
Let's solve the problem step by step.
Step 1: Let's assume the number of girls in school as 'g'.
Step 2: Given that 3/4 of the number of girls is equal to half the number of boys.
So, (3/4)g = (1/2)b, where 'b' represents the number of boys.
Step 3: We are also given that the total number of pupils in school is 1420.
Therefore, g + b = 1420.
Step 4: Now, let's substitute the value of (3/4)g from equation (2) into equation (1).
(3/4)g = (1/2)b
(3/4)g = (1/2)(1420 - g)
Step 5: Solve for 'g':
(3/4)g = (1/2)(1420 - g)
Multiply both sides by 4 to get rid of the fraction:
3g = 2(1420 - g)
Distribute:
3g = 2840 - 2g
Add 2g to both sides:
3g + 2g = 2840
Combine like terms:
5g = 2840
Divide both sides by 5:
g = 2840/5
g = 568
Step 6: Substitute the value of g into equation (2) to solve for 'b'.
g + b = 1420
568 + b = 1420
Subtract 568 from both sides:
b = 1420 - 568
b = 852
Therefore, there are 852 boys in the school.
To solve this problem, we need to set up an equation based on the given information.
Let's say the number of girls in school is represented by 'G', and the number of boys is represented by 'B'.
According to the question, "3/4 of the number of girls in school is equal to half the number of boys."
Mathematically, this can be represented as:
(3/4) * G = (1/2) * B
Now, we also know that the total number of pupils in the school is 1420. This means the sum of the number of girls and boys should be equal to 1420.
G + B = 1420
We can solve these two equations simultaneously to find the values of 'G' and 'B'.
Let's start by isolating 'G' in the first equation:
(3/4) * G = (1/2) * B
Multiply both sides by 4/3 to get rid of the fraction:
G = (4/3) * (1/2) * B
G = (2/3) * B
Now we substitute this value of 'G' in the second equation:
(2/3) * B + B = 1420
Multiply both sides by 3 to get rid of the fraction:
2B + 3B = 4260
5B = 4260
Divide both sides by 5:
B = 4260 / 5
B = 852
So, there are 852 boys in the school.