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* = 0.5

*x*In this particular question:

**Quote:**

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*.

**Quote:**

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: 1.4

*x* dollars.

100% of 1.4

*x* = 1 × 1.4

*x*Therefore the price for the customer, which is 125% of the base is:

125% of 1.4

*x* = 1.25 × 1.4

*x* = 1.75

*x*So we know that the final price is 1.75

*x* dollars. If we look at the manufacturing cost as the base, then

*x* = 100% of

*x*1.75

*x* = 175% of

*x*.

Therefore the increase is 175% – 100% = 75%.