The number of pupils in the school choir increased by 12% to 56(it seems like this is not a percent). How many pupils were there in the choir at first?
My question is, how do I create an algebraic equation for this?
Number of pupils in the school choir
percentagesword problem
Best Answer
We first convert the percent to a number: $12\% = 0.12$. This is done by dividing the percent by $100$ but, more quickly, it's just moving the decimal point two places to the left (don't forget that $12\% = 12.0\%$).
So, we know that the original choir had some number $X$ members, and that after the $12\%$ increase it now has $56$.
Thus, so far, we have
$$X + (12\% \text{ of X}) = 56$$
Well, what is "$12\%$ of $X$?" That would just be $12\%$ times $X$ (the key word being "of"). This is why we convert the $12\%$ to $0.12$. So from there, we know we have
$$X + (0.12 \times X) = 56$$
We can factor out $X$ from both of these terms, and thus obtain
$$X \times (0.12+1) = 56$$
Well, we can find $0.12 + 1$ - it's $1.12$. Thus, we get our final equation:
$$1.12 \times X = 56$$
(You might also see this written as $1.12X = 56$. I've mostly tried to keep this argument very simple and easy to follow since I'm not sure how experienced you are with math and you might not be comfortable with that notation yet.)
If you wanted to solve for $X$, you just would divide both sides by $1.12$.