A retailer sold an appliance for $80

[kyle_proctor]

A retailer sold an appliance for $80. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?

A. $10
B. $16
C. $20
D. $24
E. $25


X = original cost of appliance

(80-X) / X = 1/4X

0 = X^2 + 4X - 320

I solved and elimiated the negative root. Thus leaving answer choice B.

B is the correct answer.


I am not confident with this problem at all or my approach. Please shed some light on how you would start?

Setting up the equation was difficult for me. Any help would be greatly appreciated.

Thanks, KP

[bineeshnair4u]

Equation: Profit% = (SP-CP)/CP
=> 25/100 = (80-CP)/CP
=> 1/4 = (80/CP) - 1
=> CP = $64
Profit = $16

[RonPurewal]

X = original cost of appliance

(80-X) / X = 1/4X

0 = X^2 + 4X - 320

I solved and elimiated the negative root. Thus leaving answer choice B.

whoa, no.
first of all, note that you said "x = original cost of the appliance", but then you got x = 16. that's not the right result; the original cost of the appliance was 64, not 16.
moreover, the setup isn't right. where you have x/4, you should actually just have 1/4.

in fact, this is the most colossal example of a lucky coincidence that i have ever seen on this exam! your setup was incorrect and you identified the wrong quantity, but the stars somehow aligned in a way that landed you on the correct number. (i guess you should stop playing the lottery at this point.)

[RonPurewal]

you can also solve this problem by backsolving from the answer choices.

start in the middle, with choice (c), $20 (which not only is located in the middle of the choices but is also a "nice" number).
if the gross profit was $20, then, according to the problem, $20 is one-fourth of the original cost.
this doesn't work, because it implies that the original cost is $80 -- which implies that the retailer made no profit at all.

so, eliminate (c), and also eliminate (d) and (e) because we got a result that is too big.

now try choice (d), $16.
if the gross profit was $16, then, according to the problem, $16 is one-fourth of the original cost.
this means that the original cost was $64.
this checks perfectly with the given information: if the appliance was sold for $80, then that's a gross profit of $16, as required.

so, (b).

[kyle_proctor]

Thanks for the help guys. I knew I was wrong with this approach even though I got lucky somehow.


(80-X) / X = 1/4


So this formula above is correct then? Solving for x equals 64. Thus, the margin is 16.

I guess I was thinking I needed to solve for 1/4X instead of simply setting the profit equation equal to 1/4.

Good lesson learned. Appreciate the feedback.

[RonPurewal]

Thanks for the help guys. I knew I was wrong with this approach even though I got lucky somehow.


(80-X) / X = 1/4


So this formula above is correct then? Solving for x equals 64. Thus, the margin is 16.

that is correct.

I guess I was thinking I needed to solve for 1/4X instead of simply setting the profit equation equal to 1/4.

nah. remember that you're setting up a ratio.
if you put that x on the right-hand side, then it's suddenly not a ratio anymore; in that case, it's 1/4 of an actual quantity. if the left-hand side is a ratio, that's bad news bears.

Good lesson learned. Appreciate the feedback.

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