SOLUTION: Lee bought a book for �300 and sold it to Wong at a profit of x%. Wong then sold the same book to Fei at a profit of x%.If Fei paid �(6x+0.75) more for the book than what Lee paid,

Question 1117368: Lee bought a book for �300 and sold it to Wong at a profit of x%. Wong then sold the same book to Fei at a profit of x%.If Fei paid �(6x+0.75) more for the book than what Lee paid, find the value of x.
Found 5 solutions by Theo, greenestamps, solver91311, MathTherapy, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
this is what i get after repeated tries to understand what they mean.

x% is equal to 100x.

if the profit is x%, then the profit is 300 * x.

for example, if x% = 10, then x = .10 and the profit is 300 * .10 = 30
30/300 = .10 * 100 = 10%.

300 + 300 * x is equal to 300 * (1 + x)

lee bought it for 300.

wong paid 300 * (1 + x).

fei paid 300 * (1 + x) * (1 + x).

that means that fei paid 300 * (1 + x)^2.

fei paid 6x + .75 more than what lee paid for it.

that means that fei paid 300 + 6x + .75.

since fei also paid 300 * (1 + x)^2, then you get:

300 * (1 + x) ^ 2 = 300 + 6x + .75

since (1 + x)^2 is equal to 1 + 2x + x^2, then:

300 * (1 + 2x + x^2) = 1 + 2x + x^2

simplify to get:

300 + 600x + 300x^2 = 300 + 6x + .75

the 300 on both sides of the equation cancel out and you are left with:

600x + 300x^2 = 6x + .75

subtract the right side of the equation from both sides of the equation to get:

594x + 300x^2 - .75 = 0

reorder the terms in descending order of degree to get:

300x^2 + 592x - .75 = 0

factor this quadratic equation to get:

x = -1.9812618221237 or x = 0.0012618221237011

x can't be negative, so x has to be 0.0012618221237011 or there is no solution.

when x = 0.0012618221237011, 300 * (1 + x)^2 = 300.757570933 and 300 + 6x + .75 = 300.757570933

since they're the same, then the solution is good.

your solution is that x = 0.0012618221237011

x% is equal to 100 * x, therefore x% would be equal to 0.12618221237011%.

they didn't ask for x%, so go with the value of x = 0.0012618221237011.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

The other tutor indicated it took him several tries to try to understand what the problem meant.

I think his interpretation is not right. It's not surprising, considering the very awkward way in which the problem is stated.

It seems x is a percentage, so when Lee bought the book for 300 and sold it to Wong at a profit of x%,the price Wong paid was .

Then when Wong sold it to Fei at a profit of x%, the price Fei paid was .

Now we have the problem of trying to interpret the meaning of "Fei paid �(6x+0.75) more for the book than what Lee paid". The only interpretation I see that gives a reasonable answer is that the amount Fei paid was .

So

Graphing on a graphing calculator, or some ugly work with the quadratic formula, finds x = 6.351 to 3 decimal places.

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Let

Lee paid 300

Wong paid

Fei paid

Fei paid

So

John

My calculator said it, I believe it, that settles it

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
Lee bought a book for �300 and sold it to Wong at a profit of x%. Wong then sold the same book to Fei at a profit of x%.If Fei paid �(6x+0.75) more for the book than what Lee paid, find the value of x.

These people CLAIM to be TUTORS!! Ha, ha, ha!!!
Since Lee bought the book for �300 and sold it to WONG at a profit of x%, he sold it for:
Since Wong bought the book for , and sold it to FEI at a profit of x%, he sold it for:
======>
Amount Fei paid: Amount Lee paid: �300
We then get:

--------- Cross-multiplying

Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
Lee bought a book for �300 and sold it to Wong at a profit of x%. Wong then sold the same book to Fei at a profit of x%.
If Fei paid �(6x+0.75) more for the book than what Lee paid, find the value of x.
~~~~~~~~~~~~~~~~~~~~

1. The solution by @Theo is incorrect. His starting assumption that x% is 100x is incorrect. Actually, x% of the value is 0.01x = of the value, as everybody knows. 2. The solution by @greenetamps is incorrect. His interpretation of the condition is incorrect. 3. The solutions by the tutors @solver91311 and @MathTherapy are absolutely reasonable and correct.

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