Maths Olympiad Prep

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, 2017

Algebra Difficulty 1.6 Junior Find the answer Canada

Brodie and Ryan are driving directly towards each other. Brodie is driving at a constant speed of 50 km/h. Ryan is driving at a constant speed of 40 km/h. If they are 120 km apart, how long will it take before they meet?

Pick one

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.

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