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In a country dance there are 3 boys and 2 girls in every line.

42 boys take part in the dance

How many girls take part?

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    $\begingroup$ Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. $\endgroup$ – Julian Kuelshammer Feb 24 '13 at 14:34
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For every 3 boys there are 2 girls. So for every 6 boys there are 4 girls. 42 boys are the same as $14$ lines of $3$ boys and $2$ girls therefore there are $14*2$ girls which is $28$ as user1709828 said.

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Let $y$ represent the number of girls taking part in the dance.

We can find out the number of lines in the dance by dividing the number of boys in the dance (42) by the number of boys per line (3), or by dividing the number of girls in the dance ($y$) by the number of girls per line (2).

We know that the number of lines in the dance must be equal for boys and girls. Therefore,

$${42\over3} = {y\over 2}.$$

Can you solve this?

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This problem can be solved through ratios.

Note that the ratio from boys to girls is $3:2$ or in other words, for every $3$ boys there will be $2$ girls.

For example, if there are $9$ boys there will be $6$ girls.

Therefore, in order to calculate how many girls there were, you must set up the following ratio and solve.

$$3:2 = 42 : x$$

Which is translated into the the following equation:

$$\begin{align} & \frac{3}{2} = \frac{42}{x}\\ & 3x = 84 \\ \end{align} $$

And then all you have to do is solve for $x$. Then with this ratio, you can easily find, for example, how many girls there would be if there were 72 boys.

Note: In order to get the linear equation $3x = 84$, I simply cross multiplied, the $x$ and the $3$ and the $2$ and the $42$.

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