Ratio change after addition

Question

Year 6 at Swan School has a ratio of boys to girls 5 to 3, Three girls join the class at the start of term and the ratio changes to 10:7. How many students are in year 6 at this school after the change>

Answer 1

Since the ratio of boys to girls is given as 5 to 3, use the following to represent the number of boys and girls respectively.

Number of Boys = 5x

Number of Girls = 3x

where x is the unknown constant.

When 3 girls are added to the class, the ratio changes to 10 to 7.

Here is the equation that models that situation:

5x/(3x+3) = 10/7

This is a proportion which can be simplified by cross multiplying.

10(3x+3) =35x

30x + 30 = 35x

30 = 5x

x = 6

5(6) = 30 boys

3(6) = 18 girls

If 3 girls are added:

30/21 = 10/7