Question 1163060: Hi
A clothing shop paid $1,620 for suits to be sold at a profit of $15 each. When he had sold all but 9 suits, he had recovered the cost. Assuming that each suit cost the same,how many did he buy and how much did he pay for each one.
Thanks
Found 3 solutions by Theo, MathTherapy, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website! Hi
A clothing shop paid $1,620 for suits to be sold at a profit of $15 each. When he had sold all but 9 suits, he had recovered the cost. Assuming that each suit cost the same,how many did he buy and how much did he pay for each one.
Thanks
ONLY 1 variable is necessary here. The more variables used, the more complex this problem becomes, in MOST cases.
Let number he bought be S
Then amount he paid for each suit was: 
Amount sold to break-even: S - 9
Since profit on each was $15, then price he sold EACH of the S - 9 for, was 
We then get the following BREAK-EVEN equation: 
 ---- FOILing the left-side of equation
 ------ Multiplying by LCD, S
 ---- Factoring out GCF, 5
(S - 36)(S + 27) = 0
S - 36 = 0 OR S + 27 = 0
Number of suits he bought, or  OR S = - 27 (ignore)
Cost of each suit: 
You're right, GREENESTAMPS! Thank you. I made the correction. BTW, your answers are correct, and I've adjusted mine to match yours!
Thanks again!
Answer by greenestamps(13209)  (Show Source):
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