Question

In a sixth-grade class, the ratio of boys to girls is 3:2. How many boys and how many girls could there be in this class? Is there more than one possible answer? Explain.

How do you solve?

Answer 1

There's an infinite number of possible answers because there might be any multiplication of 3 for boys and any multiplication of 2 for girls. So, for example:

There might be 3 boys and 2 girls.
There might be 6 boys and 4 girls.
There might be 9 boys and 6 girls.
There might be 12 boys and 8 girls.
etc...

In each case the ratio stays the same - 3 : 2.

Of course there probably can't be more than a few dozens of people in one class, but theoretically we can raise the numbers up to infinite.

Answer 2

There could be 6 boys and 4 girls

There are several possible answers.

Step-by-step explanation:

Consider the provided ratio.

the ratio of boys to girls is equal to 3:2, it means that for every 2 girls in the class there will be 3 boys.

Let us assume there are 6 boys in the class.

Then the number of girls would be 4 because the ratio still have to be 3 to 2.

`(6)/(4)= (3)/(2)`

We can use algebra to figure this out or you can use logic.

The boys to girls ratio is 3:2, This can be written as:

`(boys)/(girls) =(3)/(2)`

If we multiply numerator and denominator by 2 we get.

`(boys)/(girls) =(3* 2)/(2* 2)=(6)/(4)`

That means for every 6 boys there are 4 girls, either way the ratio remains the same.

Similarly If we multiply numerator and denominator by 3 we get.

`(boys)/(girls) =(3* 3)/(2* 3)=(9)/(6)`

That means for every 9 boys there are 6 girls, and the ratio remains the same.

So there are more than one possible answer.

Hence, there are several possible answers.