Problem Solving

A retailer sold an appliance for 30 percent above cost, which represented a gross profit of $21.00. For what price did the retailer sell the appliance?

a. $27.30
b. $51.00
c. $63.00
d. $70.00
e. $91.00

Profit = revenue - cost

revenue = 1.30C, where C refers to Cost
cost = C

Profit = 1.30C - C --> 21.00 = 1.30C - C --> 21.00 = .30C --> C = 70

That means that revenue = 1.30C or 1.30(70) = 91. E.

Let Cost Price(CP)=x
Selling Price(SP) = 30% above CP
SP= 30% of x + x = 0.3x +x = 1.3x

Profit = SP - CP = 1.3x - x = 0.3 x
Its given that Profit is $21, so 21 = 0.3 x
x= 70.

SP = 1.3x = 1.3 * 70 = 91
Selling Price = $ 91.

Ans E

Let the cost price be c
profit = c + 30c/100 -c
30c/100 = 21
c = 70

the price at which appliance was sold = 70 + 70 * 30/100 = 91 (E)

let x is cp.

so 0.3x = 21=>x=70.
sp=x+profit = 70+21=91

jcnissi wrote:A retailer sold an appliance for 30 percent above cost, which represented a gross profit of $21.00. For what price did the retailer sell the appliance?

a. $27.30
b. $51.00
c. $63.00
d. $70.00
e. $91.00

Lots of good algebra, but this is a perfect question for backsolving.

Other things being equal, we should start with either B or D. A and B might seem on the small side (using common sense), so let's start with D.

If the sale price is $70.00, then the cost is $70-$21 = $49. Is 21 = 30% of 49? No, it's more than 30%, so D must be wrong.

Since 21 is more than 30% of 49, we need to increase our sales price. E is the only choice bigger than $70, so we can confidently choose E without testing it out.