A percentage discount is taken from the marked amount, so a bigger discount on a higher marked amount can still leave you paying more. Work out the amount to pay for each offer, then compare.
This lesson closes the series rates and percentages in multistep consumer questions. All shops here are invented.
How do I compare two offers?
Follow these steps for each offer.
- Write the marked amount.
- Amount to pay = marked amount × (1 − discount as a decimal).
- Compare the amounts to pay, not the percentages.
Worked example 1: two shops
Shop A sells a bag marked at RM200 with 30% off. Shop B sells a similar bag marked at RM250 with 40% off.
Shop A: 200 × 0.7 = RM140. Shop B: 250 × 0.6 = RM150.
Shop B has the larger discount, 40% against 30%, but the amount to pay is RM10 higher. The 40% was taken from a larger starting amount.
Worked example 2: one discount against two
A shirt is marked at RM400. Offer 1 is a single 40% discount. Offer 2 is 30% off, and then a further 10% off.
Offer 1: 400 × 0.6 = RM240.
Offer 2: 400 × 0.7 = 280, and 280 × 0.9 = RM252.
Offer 2 leaves RM12 more to pay. Its combined multiplier is 0.63, so the reduction is 37%, not 40%.
The mistake of trusting the headline percentage
A common slip is to pick Shop B because 40% sounds stronger. A percentage only means something when you know what it is taken from.
Fix this with one line of working per offer: marked amount, multiplier, amount to pay. Write the three numbers before you choose.
Check yourself
Item P is marked at RM150 with 40% off. Item Q is marked at RM110 with 20% off. Which leaves the smaller amount to pay?
Answer
Item P: 150 × 0.6 = RM90.
Item Q: 110 × 0.8 = RM88.
Item Q leaves RM2 less to pay, even though its discount is only 20%.
What to study next
Test the whole series in the integrated practice set. You can also revisit recovering an original amount after successive changes.
If you want a teacher to go through your comparisons, see online one-to-one Mathematics tuition.