Question

A sofa and a love seat together costs $600. The sofa costs $75 less than double the love seat. How much do they each cost The equation

Answer 1

To solve this problem we need to create an equation, where the unkown variable, x, represents the cost for the love seat. We know that the sofa costs $75 less than the love seat, therefore we have:

`y=x-75`

The cost for both pieces of furniture together is equal to $600. So if we add them we have:

`x+y=600`

We can swap the expression for y on the second equation.

`\begin{gathered} x+(x-75)=600 \\ x+x-75=600 \\ 2x-75=600 \\ 2x=675 \\ x=(675)/(2)=337.5 \end{gathered}`

Now we know that the love seat costs $337.5. We will use the first equation to find the cost of the sofa.

`y=337.5-75=262.5`

The sofa costs $262.5.