The ratio of boys to girls in a class room was 9:8. Half of the girls left the classroom, and then there were 15 more boys than girls.
A. How many children were in the classroom in the beginning?
B. How many girls left the classroom?
9 x were boys
8 x were girls
17 x total originally
4 x girls left
so then there were
9 x boys
4 x girls
13 x total
9 x - 15 = 4 x
5 x = 15
x = 3
I guess you can do 17 x and 4 x
9:8 = 18:16 = 27:24 = 36:32 = 45:40 = 54:48
Which of those ratios fits the problem?
To solve this problem, let's break it down step by step:
Step 1: Set up equations
Let's assign variables to represent the number of boys and girls in the classroom.
Let's say the number of boys is "9x" and the number of girls is "8x" (since the ratio of boys to girls is 9:8).
Step 2: Calculate the number of boys and girls after some girls left
Half of the girls left the classroom, which means the number of girls is reduced by half. Therefore, the new number of girls is "8x/2" or "4x". The number of boys remained the same, which is still "9x".
Step 3: Formulate a new equation based on the given information
We are told that after some girls left, there were 15 more boys than girls. So we can write the equation:
9x = 4x + 15
Step 4: Solve the equation
By simplifying the equation, we can solve for x:
9x - 4x = 15
5x = 15
x = 3
Step 5: Find the number of children in the classroom in the beginning (Part A)
To find the total number of children in the classroom, we can substitute the value of x back into our original equation:
Total number of children = Number of boys + Number of girls
Total number of children = 9x + 8x
Total number of children = 17x
Substituting x = 3 into the equation:
Total number of children = 17 * 3
Total number of children = 51
Therefore, there were 51 children in the classroom in the beginning.
Step 6: Find the number of girls that left the classroom (Part B)
We want to find the difference in the number of girls before and after some girls left.
Girls left = Number of girls in the beginning - Number of girls after some left
Girls left = 8x - 4x
Substituting x = 3 into the equation:
Girls left = 8 * 3 - 4 * 3
Girls left = 24 - 12
Girls left = 12
Therefore, 12 girls left the classroom.