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?
A bar of soap costs
A sponge costs
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
3 soaps and 5 sponges for $2.31
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 :)