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

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=(320-7y)/(6)\ \ \ \ (iii)`

Put this in (ii) , we get

`25((320-7y)/(6))+17y=1017\\\\\Rightarrow\ (25(320)-25(7y))/(6)+(17*6y)/(6)=1017\\\\\Rightarrow\ (8000-175y)/(6)+(102y)/(6)=1017\\\\\Rightarrow\ (8000-175y+102y)/(6)=1017\\\\\Rightarrow\ 8000-73y=6*1017\\\\\Rightarrow\ 8000-73y=6102\\\\\Rightarrow\ 73y=8000-6102\\\\\Rightarrow\ 73y= 1898\\\\\Rightarrow\ y=(1898)/(73)\\\\\Rightarrow\ y=26`

Put this in (iii),

`x=(320-7(26))/(6)=23`

Hence, Selling price of each corsage = $ 23

Selling price of each boutonniere = $26