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CEMC Gauss (Grade 8), 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 $100 is a 0.20×$100=$200.20\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 $100 is a 0.10×$100=$100.10\times \$100=\$10 discount, giving a discounted price of $100−$10=$90\$100-\$10=\$90.

A second discount of 10% on the new price of $90 is a 0.10×$90=$90.10\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 $100 is a 0.15×$100=$150.15\times \$100=\$15 discount, giving a discounted price of $100−$15=$85\$100-\$15=\$85.

A further discount of 5% on the new price of $85 is a 0.05×$85=$4.250.05\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 $100 is a 0.05×$100=$50.05\times \$100=\$5 discount, giving a discounted price of $100−$5=$95\$100-\$5=\$95.

A further discount of 15% on the new price of $95 is a 0.15×$95=$14.250.15\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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