Question

Calculate the original price of these items before the

percentage changes shown. Show all of your working.

a) A coat that costs £46.50
after a 7% price reduction

b) A jumper that costs £32.80 after a price increase of
6%
​

Answer 1

a. £50

b. £30.94

Explanation:

100-7=93

x×93/100=46.50

x×93=46.50×100=4650

x=4650/93=50 £

b.

100+6=106

y×106/100=32.80

y×100=32.80×100=3280

y=3280/106≈30.94£

Answer 2

50 and 30.94

Explanation:

• a

The coat cost 46.5 pounds after a 7 percent reduction

so we can write:

• 46.5⇒ (100-7)⇒ 93 percent
• x(the initial price) ⇒ 100 percent

using the proprtionality relation:

x= (100*46.5)/93 = 50

so the initial price of the coat is 50 pounds

• b

The jumper costs 32.8 pounds after an increase of 6 percent

so:

• 32.8⇒(100+6)⇒ 106 percent
• x (the initial price)⇒ 100 percent

using proportionality:

x= (100*32.8)/106 = 30.94

the initial price is 30.94 pounds