Expert: Paul Klarreich - 3/22/2009

Question
1. if the price of gasoline increase by 25% and Ron intends to spend only 15% more on gasoline, by what % should he reduce the quantity of petrol that he buys?
2. A merchant who marked his goods up by 50% subsequently offered a discount of 2%. What is the percentage profit that the merchant make after offering the discount?
3. by selling an article at 80% of its marked price, a merchant make a loss of 12%. What will be the % profit made by the merchant if he sells the article at 95% of its marked price?

Answer
Questioner:   Catherine
Country:  Philippines
Category:  Advanced Math
Private:  No
 
Subject:  word problems
Question:  1. if the price of gasoline increase by 25% and Ron intends to spend only 15% more on gasoline, by what % should he reduce the quantity of petrol that he buys?
2. A merchant who marked his goods up by 50% subsequently offered a discount of 2%. What is the percentage profit that the merchant make after offering the discount?
3. by selling an article at 80% of its marked price, a merchant make a loss of 12%. What will be the % profit made by the merchant if he sells the article at 95% of its marked price?


1. if the price of gasoline increase by 25%

>> That means the price is multiplied by  1.25

and Ron intends to spend only 15% more on gasoline,

>> that means the total cost is multiplied by 1.15.

by what % should he reduce the quantity of petrol that he buys?

Then the quantity is multiplied by some unknown factor, X, and

X * 1.25 = 1.15

X = 1.15/1.25 = 0.92, which is an 8% decrease.

2. A merchant who marked his goods up by 50%

>> cheap.  I mean, multiplied by a factor of 1.50

subsequently offered a discount of 2%.

>> a factor of 0.98

What is the percentage profit that the merchant make after offering the discount?

Multiply: 1.5 * 0.98 = 1.47 = a 47% increase.

3. by selling an article at 80% of its marked price,

>> that means  0.80 * Mark

a merchant make a loss of 12%.

>>  That means 0.88 * cost.

So if  0.80 * mark = 0.88 * cost.

Then  mark = 0.88/0.8 * cost, or  mark = 1.1 * cost.

What will be the % profit made by the merchant if he sells the article at 95% of its marked price?

Price = 0.95 * mark = 0.95 * (1.1 * cost) = 1.045 * cost, or 4.5%

Note:  These problems belong in one of the basic math sections.  Advanced Math is for Trig and Precalculus.