A sports shop is selling all badminton rackets at a 40% discount. Members get a further discount of $3 on every racket they buy. Farhan is a member who bought 5 rackets and paid $90 altogether. (a) How much did Farhan pay for each racket? (b) What was the price of each racket after the 40% discount but before the member discount? (c) What was the original price of each racket before any discount?

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A sports shop is selling all badminton rackets at a 40% discount. Members get a further discount of $3 on every racket they buy. Farhan is a member who bought 5 rackets and paid $90 altogether.

How much did Farhan pay for each racket?
What was the price of each racket after the 40% discount but before the member discount?
What was the original price of each racket before any discount?

Need a hint?

Work backwards. First find what one racket cost Farhan, then undo the $3 member discount before dealing with the 40%.

(a) Price paid for 1 racket = $90 ÷ 5 = $18.
(b) The member discount was $3 per racket, so the price after the 40% discount was $18 + $3 = $21.
(c) After a 40% discount, the price is 100% - 40% = 60% of the original price.
60% of the original price = $21, so 10% = $21 ÷ 6 = $3.50.
100% = $3.50 × 10 = $35.

Answer: $35

Habit

Many pupils add 40% of $21 to get $29.40, or forget to add back the $3. After a 40% discount the $21 is 60% of the original price, not 100%.