There are 48 students in a school play. The ratio of boys to girls is 5:7. How many boys are in the school play? Explain how you found your answer

Boys:  x
gilrs:   y

From the text of the task:

$$\left \{ {{\frac{x}{y}=\frac{5}{7}} \atop {x+y=48 \rightarrow x=48-y}} \right.$$

Replacing x:

$$\frac{48-y}{y}=\frac{5}{7}\\ \\ 7(48-y)=5y\\ \\ 336-7y=5y\\ \\ 12y=336\\ \\ y=\frac{336}{12}=28$$

So there are 28 girs and 20 boys

Did you say that the ratio of boys to girls is 5 to 7?

Well, then we know that 5 ’groups’ in the cast are boys, and 7 ’groups’ are girls.
So all together, there are 12 ’groups’ of students in the play, although we don’t know
how many a ’group’ is.

But wait a second.   You said there are 48 all together.   So each ’group’ must be
48/12 = 4 students.

5 ’groups’ of boys = 20 boys
7 ’groups’ of girls = 28 girls

Check:

- The ratio of 20 to 28 is 5 to 7.  OK

- 20 + 28 = 48 all together.

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