SOLUTION: 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,h

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): You can put this solution on YOUR website!

------------------------------------------------------------------
For tutor @MathTherapy....

(1) I firmly agree that the problem should be solved using a single variable.

(2) Check your solution where you factor out the LCM of 15....

------------------------------------------------------------------

Let the number of suits be x.

The cost of each suit is

The sale price of each suit is

When (x-9) suits have been sold, the total sales is equal to the original cost:

(ignore the negative solution)

ANSWERS:

He bought x=36 suits

The amount he paid for each one was $1620/x = $1620/36 = $45

CHECK: (x-9) suits, sold at 1620/x+15 each, should equal 1620:

RELATED QUESTIONS
Consider a large clothing shop in Sydney. Suppose it is known that the number of business (answered by ewatrrr)
A store owner has 225 suits. At the end of a sale he had sold 4/5 of them. How many suits (answered by richwmiller)
A clothier sold 90 suits. 1/3 at 40% off and 2/3 at 20% off the usual price. If his... (answered by stanbon)
Hans paid $1.50 each for programs to the game. He sold all but 20 of them for $3 each and (answered by ankor@dixie-net.com)
Hann paid $1.50 each for programs to the game, he sold all but 20 of them for $3 dollars... (answered by ankor@dixie-net.com)
Hans paid $1.50 ea. For programs to the game. He sold all but 20 of them for $ 3.00 ea.... (answered by jim_thompson5910)
Baka sold article for $6900 and made a profit of 15%. Calculate his profit if he had sold (answered by Edwin McCravy)
Please help! If you can show me what I did wrong, that would be helpful, thanks 1.... (answered by solver91311)
If Joshua paid for 48,000$ for all of his expenses, consiting of dresses and shoes, with... (answered by Theo)