# Claire bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. How do you find the cost of each item?

##### 1 Answer

A bar of soap costs

A sponge costs

#### Explanation:

*This question involves setting up a system of equations. If you are not familiar with systems of equations, I'd suggest you watch this video before proceeding.*

Now, to set up a system, we need variables. Let's call the **price of one soap bar** **the price of one sponge**

Claire:

3 soaps and 5 sponges for $2.31

Steve:

5 soaps and 3 sponges for $3.05

*Note: I have converted dollars to cents, simply to keep everything in whole numbers. We'll convert back to dollars in the end.*

Now we have a system. Notice, however, that nothing cancels by simply adding or subtracting equations. The common step is to manipulate one equation so that things will cancel, but doing this here will lead to a lot of messy fractions. Hence, we will manipulate *both* equations. **We will multiply Claire's equation by 5, and Steve's equation by 3.** This gives us:

Now, notice that we have a

Now, to solve for

Now that we know what

Now we have

A bar of soap (

A sponge (

Hope that helped :)