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:

$\begin{gathered} 11y=503-13x, \\ y=\frac{503}{11}-\frac{13}{11}x\text{.} \end{gathered}$

Substituting the above equation in the first one we get:

$14x+10(\frac{503}{11}-\frac{13}{11}x)=490.$

Solving for x, we get:

$\begin{gathered} 14x+\frac{5030}{11}-\frac{130}{11}x=490, \\ \frac{24}{11}x=490-\frac{5030}{11}=\frac{360}{11}, \\ 24x=360, \\ x=15. \end{gathered}$

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

$y=\frac{503}{11}-\frac{13\times15}{11}=28.$

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