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, 2019

Algebra Difficulty 1.0 Junior Prove it Canada

The Galois Restaurant is in a region that adds 10% sales tax onto the price of food and drinks purchased at a restaurant. The prices listed on their menu do not include the sales tax.

From the menu, Becky orders a plate of lasagna listed for 7.50, a side salad listed for 5.00, and a lemonade listed for $3.00. After tax is included, how much is Becky’s total bill?
A burrito is listed on the menu for 6.00. After tax is included, what is the greatest number of burritos that Jackson can buy if he has 50.00?
On the Galois Restaurant menu, hotdogs are listed at the regular price of $5.00. The restaurant has the following promotional deals:

On Mondays, if you buy a hotdog at the regular menu price of 5.00, then the price for a second hotdog is 4.50.
On Tuesdays, you pay half the tax on all hotdogs.

Chase bought two hotdogs on Monday and then two hotdogs on Tuesday. After tax is included, determine on which day Chase spent less money.

Solution

The total of the listed prices is $\$7.50+\$5.00+\$3.00=\$15.50$ .

Sales tax of 10% on $\$15.50$ is equal to $\$15.50\times 0.10=\$1.55$ .

After sales tax is included, the total of Becky’s bill is $\$15.50+\$1.55=\$17.05$ .

Alternately, we could add 10% sales tax directly to Becky’s bill by multiplying $\$15.50\times 1.10=\$17.05$ .
After 10% sales tax is included, the cost of one $6.00 burrito is$ $\$6.00\times1.10=\$6.60\$.$

At a cost of 6.60 for each burrito, the total cost of 7 burritos is $\$6.60\times7=\$46.20$ , and the total cost of 8 burritos is $\$6.60\times8=\$52.80\$.$

Since Jackson has $50.00, the greatest number of burritos that he can buy is 7.
On Monday, Chase spent $\$5.00+\$4.50=\$9.50$ plus 10% tax for two hotdogs.

Including tax, Chase spent $\$9.50\times1.10=\$10.45$ on Monday.

On Tuesday, Chase spent $\$5.00+\$5.00=\$10.00$ plus 5% tax for two hotdogs.

Including tax, Chase spent $\$10.00\times1.05=\$10.50$ on Tuesday.

Thus, Chase spent less money on Monday.

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