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Question 835001: 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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the ratio of boys to girls is equal to 3/2, this means that for every 2 girls in the class there will be 3 boys.
assume there are 2 girls in the class.
there will have to be 3 boys to keep this ratio.
the total number of children in the class would have to be 5.
assume there are 4 girls in the class.
the number of boys would have to be 6 because the ratio still have to be 3 to 2.
you can use algebra to figure this out or you can use logic.
we'll use logic.
4 girls in the class means 2 + 2
for every 2 girls in the class there are 3 boys.
number of boys in the class has to be 3 + 3
so if the class has 4 girls in it, it will have to have 6 boys in it to keep the same ratio.
if you have 6 girls in the class, the same logic applies.
number of girls is equal to 2 + 2 + 2
number of boys is equal to 3 + 3 + 3
you will have 6 girls and you will have 9 boys.
if you use algebra (not sure if you are up to that point yet), then you can solve the equation using it.
let b equal the number of boys.
let g equal the number of birls.
the ratio of boys to girls means that b/g = 3/2
solve for b to get b = 3/2 * g
if g = 2, b = 3/2 * 2 = 3
if g = 4, b = 3/2 * 4 = 6
if g = 6, b = 3/2 * 6 = 9
etc.
either way the ratio remains the same.
answer to your question about more than one possible answer is that we already have 3 possible answers and could go on forever with the only restriction being the maximum number of students that can fit into one classroom.
another restriction is that the number of girls in the classroom will have to be amultiple of 2 because if it's not, the number of boys will not be an integer and that is not possible.
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