Respuesta :
Define the variables: Let "x" be the women's shoes sold and Let "y" be the men shoes sold
Write a system of inequalities to represent this situation:
[tex]x + y\geq 15\\\\2.50x + 3y\geq 60[/tex]
Two possible solution are (x, y) = (15, 10) and (20, 15)
Solution:
Let "x" be the women's shoes sold
Let "y" be the men shoes sold
From given,
Commission cost for each pair of women's shoes = $ 2.50
Commission cost for each pair of mens shoes = $ 3
To meet his sales targets, he must sell at least 15 pairs of shoes total
"at least" means he can sell 15 pairs or greater than 15 also
Thus we frame a inequality as:
[tex]x + y\geq 15[/tex]
He also wants to make at least $60 a week in commissions
Thus we frame a inequality as:
[tex]2.50 \times x + 3 \times y\geq 60\\\\2.50x + 3y\geq 60[/tex]
Thus system of inequalities to represent this situation is:
[tex]x + y\geq 15\\\\2.50x + 3y\geq 60[/tex]
Two possible solutions are:
Substitute x = 15 and y = 10
[tex]15 + 10\geq 15\\\\25\geq 15[/tex]
Thus first inequality is satisfied
[tex]2.50 \times 15 + 3 \times 10\geq 60\\\\37.5 + 30\geq 60\\\\67.5\geq 60[/tex]
Thus second inequality is also satisfied
Thus one possible solution is x = 15 and y = 10
Substitute x = 20 and y = 15
[tex]20 + 15\geq 15\\\\35\geq 15[/tex]
Thus first inequality is satisfied
[tex]2.50 \times 20 + 3 \times 15\geq 60\\\\50 + 45\geq 60\\\\95\geq 60[/tex]
Thus second inequality is also satisfied
Thus another possible solution is x = 20 and y = 15
