The ratio of boys to girls is 3 to 7. If there are 20 more girls than boys, how many boys are there?
There are 17 boys
Not quite.
b/g = 3/7
g = b+20
b = g-20
= 7b/3 - 20
4b/3 = 20
b = 15
check: 15/35 = 3/7
To solve this problem, let's set up a system of equations based on the given information.
Let's assume the number of boys is represented by 'x' and the number of girls is represented by 'y'.
According to the given information, the ratio of boys to girls is 3 to 7, which can be written as:
x/y = 3/7
Also, it is given that there are 20 more girls than boys. This can be written as:
y = x + 20
Now, we can solve this system of equations.
First, let's express 'x' in terms of 'y' from the second equation:
x = y - 20
Substituting this value of 'x' in the first equation:
(y - 20) / y = 3/7
Now, we can cross-multiply:
7(y - 20) = 3y
Expanding the equation:
7y - 140 = 3y
Bringing like terms to one side:
7y - 3y = 140
Simplifying:
4y = 140
Dividing both sides by 4:
y = 35
Therefore, there are 35 girls.
Now, substituting this value of 'y' in the equation y = x + 20:
35 = x + 20
Subtracting 20 from both sides:
x = 35 - 20
x = 15
Therefore, there are 15 boys.
So, there are 15 boys in total.