Question35. At a festival, of the number of girls was equal to of the number of boys. There were 165 fewer boys than girls, how many children were at the festival in all?
Studdy Solution
STEP 1
1. Let represent the number of girls at the festival.
2. Let represent the number of boys at the festival.
3. of the number of girls is equal to of the number of boys.
4. There are 165 fewer boys than girls.
STEP 2
1. Set up equations based on the problem statement.
2. Solve the system of equations to find the number of girls and boys.
3. Calculate the total number of children at the festival.
STEP 3
Set up equations based on the problem statement.
From the problem, we have:
And, there are 165 fewer boys than girls:
STEP 4
Solve the system of equations to find the number of girls and boys.
First, solve the first equation for one variable. Let's solve for :
Multiply both sides by 35 to eliminate the fractions:
Now, solve for :
Substitute this expression for into the second equation:
Clear the fraction by multiplying through by 21:
Rearrange to solve for :
Divide both sides by 11:
Now, substitute back into the equation for :
STEP 5
Calculate the total number of children at the festival.
The total number of children is the sum of the number of girls and boys:
The total number of children at the festival is:
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