# Translating a word problem into an algebraic equation and then solving for it.

Elizabeth bought five bags of candy for Halloween. Forty-eight children visited her home and she gave each child three pieces of candy. At the end of the night she still had one bag of candy. How many pieces of candy were in each bag?

I actually know how to solve this pretty easily, but it asks to set up an equation and it also asks what x represents.

The way I did it was just take $48\cdot3=144$ pieces of candy, then I divided it by 4 since she used 4 bags of candy up to get $36$. Again, I am not sure how to set an equation up here. It just seems easier to go about it this way.

• I don't see anything wrong with your method....it seems optimal. – lulu Feb 5 '17 at 17:43
• I agree, but the question asks to set up an equation. – PiFarmer86 Feb 5 '17 at 17:45
• To translate your method into more symbolic form: let $N$ be the number per bag. Then we get $4N=48\times 3\implies N=12\times 3=36$. – lulu Feb 5 '17 at 17:50

## 3 Answers

Let $b$ be the number of candies per bag,$$5b-48\cdot3=b.$$

The solution is

$$b=\frac{48\cdot3}4=36.$$

X = number of candies per bag.

$4(bags)*X(candies/bag) = 48(children) * 3(candies/children) = 144 (candies)$

So X = 36 (candies/bag)

And you can see that all the units work out.

If you set the number of candies in each bag be $x$, you can represent the initial and final number of candies in terms of $x$, thus writing an equation.