Maths Olympiad Prep

Library / /119 of 183

, 2017

Algebra Difficulty 1.6 Junior Find the answer Canada

Sara goes to a bookstore and wants to buy a book that is originally priced at $100. Which of the following options gives her the best discounted price?

A discount of 20%\text{A discount of 20\%}
A discount of 10%, then a discount of 10% off the new price\text{A discount of 10\%, then a discount of 10\% off the new price}
A discount of 15%, then a discount of 5% off the new price\text{A discount of 15\%, then a discount of 5\% off the new price}
A discount of 5%, then a discount of 15% off the new price\text{A discount of 5\%, then a discount of 15\% off the new price}
All four options above give the same price\text{All four options above give the same price}

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

A discount of 20% on a book priced at 100isa100 is a 0.20×0.20\times \$100=\$20$ discount.

Thus for option (A), Sara’s discounted price is $100−$20=$80\$100-\$20=\$80.

A discount of 10% on a book priced at 100isa100 is a 0.10×0.10\times \$100=\$10discount,givingadiscountedpriceof discount, giving a discounted price of \$100-\$10=\$90$.

A second discount of 10% on the new price of 90isa90 is a 0.10×0.10\times \$90=\$9$ discount.

Thus for option (B), Sara’s discounted price is $90−$9=$81\$90-\$9=\$81.

A discount of 15% on a book priced at 100isa100 is a 0.15×0.15\times \$100=\$15discount,givingadiscountedpriceof discount, giving a discounted price of \$100-\$15=\$85$.

A further discount of 5% on the new price of 85isa85 is a 0.05×0.05\times \$85=\$4.25$ discount.

Thus for option (C), Sara’s discounted price is $85−$4.25=$80.75\$85-\$4.25=\$80.75.

A discount of 5% on a book priced at 100isa100 is a 0.05×0.05\times \$100=\$5discount,givingadiscountedpriceof discount, giving a discounted price of \$100-\$5=\$95$.

A further discount of 15% on the new price of 95isa95 is a 0.15×0.15\times \$95=\$14.25$ discount.

Thus for option (D), Sara’s discounted price is $95−$14.25=$80.75\$95-\$14.25=\$80.75.

Therefore, the four options do not give the same price and option (A) gives Sara the best discounted price.

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.