Question 1163060
let c be the cost of each suit.
let s be the selling price of each suit.
then xc = total cost and xs = total selling price.
you are given that 1620 is the total cost.
this means that xc = 1620
you are given that the total cost is achieved when all but 9 suits are sold.
this means that xc = (x - 9) * s.
since xc = 1620, you get:
1620 = (x - 9) * s
you are given that the profit on each suit is 15.
this means s = c + 15
therefore:
1620 = (x - 9) * (c + 15)
simplify this to get:
1620 = xc + 15x - 9c - 15*9
simplify further to get:
1620 = xc + 15x - 9c - 135
since xc = 1620, this becomes:
1620 = 1620 + 15x - 9c - 135
subtract 1620 from both sides of this equation to get:
0 = 15x - 9c - 135
add 35 to both sides of this euation to get:
135 = 15x - 9c
since xc = 1620, then c must be equal to 1620 / x
replace c with 1620/x to get:
135 = 15x - 9*1620/x
multiply both sides of this equation by x to get:
135x = 15x^2 - 14580
subtract 135x from both sides of the equation to get:
0 = 15x^2 - 135x - 14580
divide both sides of this equation by 15 to get:
0 = x^2 - 9x - 972
factor this equation to get:
(x + 27) * (x - 36) = 0
solve for x to get:
x = 36 or x = -27
x has to be positive, so x = 36.
go back to your original equations to get:
xc = 36*x = 1620
solve for c to get c = 45.
since s = c + 15, then s = 60.
your total cost is when all but 9 suits are sold.
this means that (x-9) * 60 = 1620
since x = 36, this becomes 27 * 60 = 1620 which becomes 1620 = 1620.
this confirms that x = 36 is correct.
the cost for each suit is 1620/36 = 45.
that's your solution.