There are 160 people in a grade. The ratio of boys to girls is 3 to 5. Write a proportion you can use to find the number of boys.
number of boys --- b
number of girls ---- 160-b
b : 160-b = 3 : 5
or
b/(160-b) = 3/5 <------- that's what you asked for
There are 160 people in a grade. The ratio of boys to girls is 3 to 5. Which proportion can you use to find the number x of boys?
To find the number of boys in the grade, we can set up a proportion using the given ratio of boys to girls.
Since the ratio of boys to girls is 3 to 5, we can write the proportion as follows:
Boys/Total number of students = 3/5
Now, we know that the total number of students in the grade is 160. So we substitute the value into the proportion:
Boys/160 = 3/5
To solve for the number of boys, we need to isolate the variable 'Boys' on one side of the equation. We can do this by cross-multiplication:
5 * Boys = 3 * 160
Simplifying the equation:
5 * Boys = 480
Now, divide both sides of the equation by 5 to solve for 'Boys':
Boys = 480/5
Finally, we can calculate the value:
Boys = 96
Therefore, there are 96 boys in the grade.
b = boys
g = girls
There are 160 people in a grade means:
b + g = 160
Subtract b to both sides
g = 160 - b
The ratio of boys to girls is 3 to 5 means:
b / g = 3 / 5
Replace g with 160 - b in this equation.
b / ( 160 - b ) = 3 / 5
This is a proportion.
The solution is:
Cross multiply a proportion.
5 b = 3 ( 160 - b )
5 b = 480 - 3 b
Add 3 b to both sides
8 b = 480
b = 480 / 8
b = 60
g = 160 - b =160 - 60
g = 100
Check result:
b + g = 60 + 100 = 160
b / g = 60 / 100 = 20 • 3 / 20 • 5 = 3 / 5