Question

Work out the percentage change when a price of £65 is decreased to £39.

Answer 1

p = 40%

Explanation:

65 - p%65 = 39

65 - 65p/100 = 39

6500 - 65p = 3900

6500 - 3900 = 65p

65p = 2600

p = 2600 : 65

p = 40%

Answer 2

40% decrease

Explanation:

Say the percent decrease is x%. Then, we can write the equation:

65 - x% * 65 = 39

Notice that 65 is a common factor of both terms on the left, so factor that out:

65 * (1 - x%) = 39

Divide by 65 on both sides:

1 - x% = 0.6

Subtract 0.6 from and add x% to both sides:

x% = 0.4

Remember that % simply means "out of 100", so x% = x/100:

x/100 = 0.4

Multiply by 100:

x = 40

So the percentage decrease is 40%, or the percent increase is -40% (whichever way the question asks).

Hope this helps!