Question

There are 24 students in Juan’s class. The ratio of girls to boys is $1:2$. How many girls and boys are in Juan’s class?

Answer 1

Hint:In order to express a mathematical problem explained in words we have to take all the relevant and important information mentioned in the word problem and represent it in a much easier way like an equation. After representing it in the symbolic form we have performed the basic arithmetic operations as specified in the question. Eventually we would be able to solve the question. So by using the above definition and techniques we can solve the given question.

Complete step by step solution:
Given statements:
$
{\text{Total number of students: 24}}...........................\left( i \right) \\
{\text{Ratio of girls to boys:}}\;1:2{\text{ }}...................\left( {ii} \right) \\
$
Now we need to find the number of girls and boys in Juan’s class.
So first let’s assume that the: ${\text{number of girls}}\;{\text{be}}\;x$
Now we know that ${\text{ratio of girls to boys:}}\;1:2{\text{ }}$
Such that we can write:
${\text{number of boys = }}\;2x$
Also it’s given that:
${\text{Total number of students: 24}}$
So we can write:
$x + 2x = 24...............................\left( {iii} \right)$
Now on solving for$x$ we can find the number of girls and thereby the number of boys.
So solving (iii):
We can write:
$
x + 2x = 24 \\
3x = 24 \\
x = \dfrac{{24}}{3} \\
x = 8....................................\left( {iv} \right) \\
$
Therefore the number of girls would be 8.
Now to find the number of boys we have:
\[
\Rightarrow {\text{number of boys = }}\;2x \\
\Rightarrow {\text{number of boys = }}\;2 \times 8 \\
\Rightarrow {\text{number of boys = }}\;16 \\
\]
Therefore there would be 8 girls and 16 boys in Juan’s class.

Note: On solving similar algebraic word problems, it’s advisable to adopt the above prescribed method since it’s easy to understand and execute. Also while solving word problems it’s important to read the question properly. After reading the question properly one has to separate the relevant and irrelevant information carefully.