Question

The ratio of girls to boys in a grade is 6 to 5. If there are 24 girls in the grade then howmany students are there altogether?

Answer 1

The given information is that the ratio of girls to boys in a grade is:

`6\colon5`

And you need to find if there are 24 girls in the grade, how many students are there altogether.

Knowing the ratio, we can find how many boys there are (let's call it x), then:

`\begin{gathered} 6\colon5=24\colon x \\ \rightarrow(6)/(5)=(24)/(x) \end{gathered}`

Now solve for x:

`\begin{gathered} \text{Multiply both sides by x} \\ x(6)/(5)=x(24)/(x) \\ \text{Simplify} \\ x(6)/(5)=24 \\ \text{Multiply both sides by 5}/6 \\ x(6)/(5)\cdot(5)/(6)=24\cdot(5)/(6) \\ \text{Simplify} \\ x=(24*5)/(6)=(120)/(6) \\ x=20 \end{gathered}`

Thus, if there are 24 girls in the grade, there are 20 boys too, there are altogether 24 girls+20 boys=44 students