Word problems with variables on both sides

Question

Suppose your club is selling candles to raise money. it costs $100 to rent a booth from which to sell the candles. If the candles cost your club $1 each and are sold for $5 each how many candles must be sold to equal your expense?

Answer 1

This is a break-even problem.

 

Let 5x = Revenue from selling each candle

Let 1x + 100 (or x + 100) = the expense for selling candles

 

So, set these equal to each other:

 

5x = x + 100

 

Subtract 1x from both sides, to get:

 

4x = 100

 

Divide both sides by 4

 

x = 25

 

So, the break-even in units is sell 25 candles, in order to cover the expenses