The number of girls is 5 8 of the number of boys. If there are 442 children together, how many more boys than girls are there?
Let's say the number of boys is x.
The number of girls is 5/8*x = (5/8)*x = (5/8)*442 = 0.625*442 = 276.25
The boys are x = 442-276.25 = <<442-276.25=165.75>>165.75 more than the girls. Answer: \boxed{165.75}.
To solve this problem, let's set up an equation.
Let's say the number of boys is x.
According to the problem, the number of girls is 5/8 of the number of boys, which can be written as 5/8 * x.
Now, we know that the total number of children is 442. So, we can set up the equation:
x + 5/8 * x = 442
To solve this equation, we need to find a common denominator for the fractions. The common denominator is 8.
So, we can rewrite the equation as:
(8/8)x + (5/8)x = 442
Combining like terms, we get:
(13/8)x = 442
Now, to solve for x, we multiply both sides by the reciprocal of 13/8, which is 8/13:
x = (442 * 8)/13
x ≈ 272 (rounded to the nearest whole number)
Therefore, the number of boys is approximately 272.
To find the number of girls, we can substitute the value of x into the expression 5/8 * x:
Number of girls = 5/8 * 272
Number of girls ≈ 170 (rounded to the nearest whole number)
Now, to find the difference between the number of boys and girls:
Difference = number of boys - number of girls
Difference = 272 - 170
Difference = 102
Therefore, there are 102 more boys than girls.
Let's solve this step-by-step:
Step 1: Let's assume the number of boys as "x".
Step 2: According to the given information, the number of girls is 5/8 of the number of boys.
Step 3: Therefore, the number of girls can be calculated as (5/8) * x.
Step 4: The total number of children is given as 442.
Step 5: Since the total number of boys and girls together is 442, we can write the equation: x + (5/8) * x = 442.
Step 6: Combining like terms, we simplify the equation to (13/8) * x = 442.
Step 7: To solve for x, we multiply both sides of the equation by 8/13, giving x = (8/13) * 442 = 272.
Step 8: The number of girls can then be found by multiplying (5/8) by x, giving (5/8) * 272 = 170.
Step 9: To find the difference between the number of boys and girls, we subtract the number of girls from the number of boys: 272 - 170 = 102.
Therefore, there are 102 more boys than girls.