A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 25 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
A. 65% B. 70% C. 75% D. 85% E. 95%
(C) Since a 40% increase price is the same as multiplying the original amount by 1.4, the retail store paid 1.4 times the cost of manufacturing the jeans. The customer then paid 25% more than this amount, or 1.25 times it. So the customer paid 1.25 × 1.4 × the cost to manufacture, or 1.75 × the cost to manufacture. 1.75 times the manufacturing cost is a 75% increase in price. The correct answer is choice (C).
Alternative Method (Picking Numbers): If you are having problems with percent increases (or decreases), and you are not given a dollar amount to work with, try substituting a round number, such as 100. This allows you to make calculations that will result in clear-cut amounts. If the jeans cost $100 to make, then the retailer bought them for $140 (40% more than $100). The customer would then buy them for 25% more than $140, or $175 (to calculate a 25% increase, multiply $140 by 1.25). Subtract $100 (the original purchase price) from $175 to get an increase in price of $75, which is a percent increase of 75%. -------------
The question outlined: The customer bought the pair of jeans for 25% more than the retailer PAID for them. Not 25% more then the retailer SOLD it for. Therefore I am not too clear on the answer.
When you deal with percentages you should keep in mind both variants of notation: 40% = 0.4 140% = 1.4 75% = 0.75 175% = 1.75 100% = 1
You should also keep in mind that percentage is a relative value. For example, if x is 200% of y, then y is 50% of x. x = 2 × y y = (1/2) × x y = 0.5x
In this particular question:
A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans.
If it cost x dollars to manufacture the pair of jeans, then the base is x. x = 100% of x = 1 × x. The price is 140% of the manufacturing cost. 140% of x = 1.4 × x.
A customer bought the pair of jeans for 25 percent more than the retailer paid for them.
The base in this case is the price, which was paid by the retailer: 1.4x dollars. 100% of 1.4x = 1 × 1.4x Therefore the price for the customer, which is 125% of the base is: 125% of 1.4x = 1.25 × 1.4x = 1.75x
So we know that the final price is 1.75x dollars. If we look at the manufacturing cost as the base, then x = 100% of x 1.75x = 175% of x. Therefore the increase is 175% – 100% = 75%.
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