SOLUTION: 1. A merchant buys goods at 25% off the list price. He desires to mark the goods so that he can give a discount of 20% on the marked price and still clear a profit of 25% on the se

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 1. A merchant buys goods at 25% off the list price. He desires to mark the goods so that he can give a discount of 20% on the marked price and still clear a profit of 25% on the se      Log On


   

Question 304956: 1. A merchant buys goods at 25% off the list price. He desires to mark the goods so that he can give a discount of 20% on the marked price and still clear a profit of 25% on the selling price. What percent of the list price must he mark the goods?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Let C equal the cost.
Let L equal the list price.

C = L - .25*L = (1-.25)*L = .75*L

Let S equal the selling price.
Let M equal the markup price.

S = M - .2*M = (1-.2)*M = .8*M

Let P = Profit Ratio

P = (S-C)/C

The question is:

What percent of the List Price must he mark the goods in order to make 25% profit.

Percent divided by 100% equals ratio.

Profit ratio = 25% / 100% = .25

We replace P above with .25 to get:

.25 = (S-C)/C

We want to make everything in terms of L which is the List Price.

Since C = .75*L, we replace C with .75*L to get:

.25 = (S-.75*L)/.75*L

We want to know what percent of the list price he must mark the goods.

We let E equal the ratio of the List Price we are looking for.

Our equation for the markup price becomes:

M = E*L

This means that the markup price is equal to E times the List Price.

Our latest revised equation is:

.25 = (S-.75*L)/.75*L

We know that S = .8*M from above.

We replace M with E*L to get S = .8*E*L and replace S with that in our equation to get:

.25 = (.8*E*L-.75*L)/.75*L

We are looking to solve for E in relation to L.

Multiply both sides of the equation by .75*L to get:

.25*.75*L = .8*E*L - .75*L

Add .75*L to both sides of the equation to get:

.25*.75*L + .75*L = .8*E*L

Divide both sides of the equation by .8*L to get:

(.25*.75*L + .75*L)/.8*L = E

We simplify to get:

(.1875*L + .75*L)/.8*L = E

We simplify further to get:

(.9375*L/.8*L = E

We simplify further to get:

E = 1.171875

We now have enough information to solve the problem.

We know that M = E*L

We replace E with 1.171875 to get:

M = 1.171875*L

We know that S = .8*M

We replace M with 1.171875*L to get:

S = .8*1.171875*L = .9375*L

We know that C = .75*L

We know that P = (S-C)/C

We replace S with .9375*L and we replace C with .75*L to get:

P = (.9375*L - .75*L) / (.75*L)

We simplify to get:

P = .1875*L / .75*L

We simplify further to get:

P = .25

Our profit ratio is equal to .25

Multiply that by 100% to get a Percent Profit of .25 * 100% = 25%

This is what we are looking for, so we are done.

Out answer is that the markup price is equal to 1.171875 times the list price.

We test our answer to determine if it is correct.

Assume the list price is any number.

We'll assume the list price is equal to $500.00

The cost is equal to .75*500 = $375.00

The markup price is equal to 1.171875*500 = $585.9375

We take 20% off the markup price to get a selling price of $468.75

Our profit ie equal to $468.75 minus $375.00 which equals $93.75

Our profit margin is equal to $93.75 / $375.00 which equals .25

Our profit percent is equal to .25 * 100% which equals 25%.

The answer is confirmed as good.

The question is what percent of the list price must he mark up the goods.

The markup ratio is 1.171875.

Multiply that by 100% to get a marked up percent of 117.1875%

Subtract 100% from that to get 17.1875%

The list price must be marked up by 17.1875% in order to achieve a profit of 25% on the selling price.

The markup price is 117.1875% of the list price.

The markup is 17.1875% of the list price.