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
[tex]18x+21y= 960\ \ \ \ (i)\\\\ 25x+17y= 1017\ \ \ \ (ii)[/tex]
Divide (i) by 3, we get
[tex]6x+7y=320\\\\\Rightarrow\ 6x=320-7y\\\\\Rightarrow\ x=\dfrac{320-7y}{6}\ \ \ \ (iii)[/tex]
Put this in (ii) , we get
[tex]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[/tex]
Put this in (iii),
[tex]x=\dfrac{320-7(26)}{6}=23[/tex]
Hence, Selling price of each corsage = $ 23
Selling price of each boutonniere = $26
