Question

Gabby has a home-based business making corsages and boutonnieres for school dances. Last year, she sold 14 corsages and 10 boutonnieres, which brought in a total of $490. This year, she sold 13 corsages and 11 boutonnieres, for a total of $503. How much does each item sell for?

Answer 1

Let x be the cost of one corsage, and y be the cost of one boutonniere, then we can set the following system of equations:

`\begin{gathered} 14x+10y=490, \\ 13x+11y=503. \end{gathered}`

Solving the second equation for y, we get:

`\begin{gathered} 11y=503-13x, \\ y=(503)/(11)-(13)/(11)x\text{.} \end{gathered}`

Substituting the above equation in the first one we get:

`14x+10((503)/(11)-(13)/(11)x)=490.`

Solving for x, we get:

`\begin{gathered} 14x+(5030)/(11)-(130)/(11)x=490, \\ (24)/(11)x=490-(5030)/(11)=(360)/(11), \\ 24x=360, \\ x=15. \end{gathered}`

Substituting x=15 in the equation that we solved for y we get:

`y=(503)/(11)-(13*15)/(11)=28.`

Answer: A corsage sells for $15, and a boutonniere sells for $28.