Question

Edna has a home-based business making corsages and boutonnieres for school dances. Last year, she sold 18 corsages and 21 boutonnieres, which brought in a total of $960. This year, she sold 25 corsages and 17 boutonnieres, for a total of $1,017. How much does each item sell for?

Answer 1

Answer: Selling price of each corsage = $ 23

Selling price of each boutonniere = $26

Step-by-step explanation:

Let x =Selling price of each corsage.

y = Selling price of each boutonniere.

As per given, we have

$18x+21y= 960\ \ \ \ (i)\\\\ 25x+17y= 1017\ \ \ \ (ii)$

Divide (i) by 3, we get

$6x+7y=320\\\\\Rightarrow\ 6x=320-7y\\\\\Rightarrow\ x=\dfrac{320-7y}{6}\ \ \ \ (iii)$

Put this in (ii) , we get

$25(\dfrac{320-7y}{6})+17y=1017\\\\\Rightarrow\ \dfrac{25(320)-25(7y)}{6}+\dfrac{17\times6y}{6}=1017\\\\\Rightarrow\ \dfrac{8000-175y}{6}+\dfrac{102y}{6}=1017\\\\\Rightarrow\ \dfrac{8000-175y+102y}{6}=1017\\\\\Rightarrow\ 8000-73y=6\times1017\\\\\Rightarrow\ 8000-73y=6102\\\\\Rightarrow\ 73y=8000-6102\\\\\Rightarrow\ 73y= 1898\\\\\Rightarrow\ y=\dfrac{1898}{73}\\\\\Rightarrow\ y=26$

Put this in (iii),

$x=\dfrac{320-7(26)}{6}=23$

Hence, Selling price of each corsage = $ 23

Selling price of each boutonniere = $26