Question

What are the two equations and variables for this word problem?

An artist is going to sell two sizes of prints at an art fair. The artist will charge $20 for a small print and $45 for a large print. The artist would like to sell twice as many small prints as large prints. The booth the artist is renting for the day costs $510. How many of each size print must the artist sell in order to break even at the fair?

Answer 1

number of large prints=6, and number of small prints=12

Explanation:

let the number large prints sold be represented by L, the number of small prints sold be represented by s.

This equation can be used to find the number of prints `510=45(L)+20(s)`

If the artist wants to sell twice as many small prints as large prints, that would be represented by `2L=s`

Substitute `s` with `2L`

`510=45(L)+20(2L)`

simplify the terms as much as possible
`510=45(L)+40(L)`

you can now combine them
`510=85(L)`

Divide, and solve for `L`
`L=6`

Now that we have the number of large prints, we can find the number of small prints using `2L=s` again
`2(6)=s`
`s=12`

Plug your answers for `L` and `s` into the original equation to check your work
`510=45(6)+20(12)`
`510=270+240`
`510=510`