Let x be the number of students in the senior class.
Four-fifths of this number x is equal to 324 based on the first sentence and the beginning of the second sentence.
So the equation to set up is [tex]\boldsymbol{\frac{4}{5}x = 324}[/tex] and it's the same as writing [tex]\boldsymbol{\frac{4x}{5} = 324}[/tex]
If you want, you can stop reading here and attempt to solve on your own.
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On the other hand, if you want to know how to solve, then read on.
The '5' in the denominator means we're dividing 4x over 5.
To get that 5 to the other side, we'll multiply both sides by 5 to undo the division operation.
[tex]\frac{4x}{5} = 324\\\\
5*\frac{4x}{5} = 5*324\\\\
4x = 1620\\\\[/tex]
Then to fully isolate x, i.e. get x all by itself, then we'll divide both sides by 4. This is to undo the multiplication of 4 onto x.
So,
[tex]4x = 1620\\\\
\frac{4x}{4} = \frac{1620}{4}\\\\
x = 405[/tex]
This means there are 405 seniors overall.
4/5 of them went to prom, so (4/5)*405 = 324 went to prom. This confirms the answer.
