# How many boys must join the group to make the ratio 5:3

#### SaltyPoro

##### New member
The question is as follows: "In a group of 48 children, the ratio of boys to girls is 3:5. How many boys must join the group to make the ratio of boys to girls 5:3."
I know the current number of boys to girls is 18:30 and that the number of girls should stay the same. But I don't know how to get the number of boys that have to join, how would you do it without guess and check?

#### ksdhart2

##### Full Member
The question is as follows: "In a group of 48 children, the ratio of boys to girls is 3:5. How many boys must join the group to make the ratio of boys to girls 5:3."
I know the current number of boys to girls is 18:30 and that the number of girls should stay the same. But I don't know how to get the number of boys that have to join, how would you do it without guess and check?
So, we're going to add some number of boys to the class. We don't know how many, but we can assign a variable to it anyway. Let's call that unknown number x. After adding the boys, there will be 18 + x boys in the class, and a total of 48 + x students. We want the ratio of boys to girls to be five to three. That means for every five boys, there needs to be three girls. Suppose the class had only 8 students and it was in this ratio. How many boys would there be? Now suppose the class had 16 students and was in this ratio. How many boys would there be then? How did you figure out these answers? What does that suggest about the proportion of the class that must be boys after adding x boys? Using that knowledge, can you set up an equation to model the fact that 18 + x must be (that proportion) of 48 + x students?

#### SaltyPoro

##### New member
So, we're going to add some number of boys to the class. We don't know how many, but we can assign a variable to it anyway. Let's call that unknown number x. After adding the boys, there will be 18 + x boys in the class, and a total of 48 + x students. We want the ratio of boys to girls to be five to three. That means for every five boys, there needs to be three girls. Suppose the class had only 8 students and it was in this ratio. How many boys would there be? Now suppose the class had 16 students and was in this ratio. How many boys would there be then? How did you figure out these answers? What does that suggest about the proportion of the class that must be boys after adding x boys? Using that knowledge, can you set up an equation to model the fact that 18 + x must be (that proportion) of 48 + x students?
So if the ratio is 5:3, and there are 30 girls, you get to 30 by multiplying 3 by 10, so I'm assuming you're meant to do the same with the 5?
If there are 50:30 boys and 18 boys originally, you minus the 50 by the old amount(18) to get the amount of boys added to the class.
So 32 boys are added to the class?

#### ksdhart2

##### Full Member
Yes, that's correct. Good job.