Please help...
The ratio of the number of boys to that of girls in Class A is 2 : 3. The ratio of the number of girls who wear glasses to the number of girls who do not wear glassesis 1:3. If there are 12 more girls than boys, how many girls wear glasses?
let the number of boys be 2x
let the number of girls be 3x
(notice boys:girls = 2x:3x = 2:3 )
given: 3x - 2x = 12
x = 12
so we know there were 24 boys and 36 girls
let the number of girls who wear glasses be y
let the number of girls who don't wear glasses be 3y
y + 3y = 36
4y = 36
y = 9
So 9 girls wear glasses
To find the number of girls who wear glasses, we need to follow these steps:
Step 1: Determine the number of boys and girls in Class A.
Let's assume the number of boys in Class A is 2x and the number of girls is 3x.
Step 2: Set up an equation using the information given in the problem.
From the information given, we know that there are 12 more girls than boys. This can be expressed as:
3x = 2x + 12
Step 3: Solve the equation to find the value of x.
By subtracting 2x from both sides of the equation, we get:
3x - 2x = 12
x = 12
Step 4: Calculate the number of girls in Class A.
Substituting the value of x into the expression for the number of girls, we get:
Number of girls = 3x = 3 * 12 = 36
Step 5: Determine the number of girls who wear glasses.
Given that the ratio of the number of girls who wear glasses to the number of girls who do not wear glasses is 1:3, we can calculate the number of girls who wear glasses:
Number of girls who wear glasses = (1 / (1 + 3)) * 36 = (1/4) * 36 = 9
Therefore, there are 9 girls in Class A who wear glasses.