A furniture store purchased a dining room table and marked it up 150% from the original cost of $456. A week later, the store placed the dining room table on sale for 30% off. What was
the discount price?

Step-by-step explanation:

Identify what you are asked to find.What is the sales tax?

Choose a variable to represent it.Let t = sales tax.

Write a sentence that gives the information to find it.The sales tax is 6.5% of the purchase price.

Translate into an equation. (Remember to change the percent to a decimal).

Simplify.t = 25.48

Check: Is this answer reasonable?Yes, because the sales tax amount is less than 10% of the purchase price.

Write a complete sentence that answers the question.The sales tax is $25.48.

(b)

Identify what you are asked to find.What is the total cost of the bicycle?

Choose a variable to represent it.Let c = total cost of bicycle.

Write a sentence that gives the information to find it.The total cost is the purchase price plus the sales tax.

Translate into an equation. (Remember to change the percent to a decimal).

Simplify.c = 417.48

Check: Is this answer reasonable?Yes, because the total cost is a little more than the purchase price.

Write a complete sentence that answers the question.The total cost of the bicycle is $417.48.

Exercise  6.3.1 :

Find (a) the sales tax and (b) the total cost: Alexandra bought a television set for $724 in Boston, where the sales tax rate was 6.25% of the purchase price.

Answer a

Answer b

Exercise  6.3.2 :

Find (a) the sales tax and (b) the total cost: Kim bought a winter coat for $250 in St. Louis, where the sales tax rate was 8.2% of the purchase price.

Answer a

Answer b

Example  6.3.2 :

Evelyn bought a new smartphone for $499 plus tax. She was surprised when she got the receipt and saw that the tax was $42.42. What was the sales tax rate for this purchase?

Solution

Identify what you are asked to find.What is the sales tax rate?

Choose a variable to represent it.Let r = sales tax.

Write a sentence that gives the information to find it.What percent of the price is the sales tax?

Translate into an equation.

Divide.

499r499=42.42499(6.3.1)

Simplifyr = 0.085

Check. Is this answer reasonable?Yes, because 8.5% is close to 10%. 10% of $500 is $50, which is close to $42.42.

Write a complete sentence that answers the question.The sales tax rate is 8.5%.

Exercise  6.3.3 :

Diego bought a new car for $26,525. He was surprised that the dealer then added $2,387.25. What was the sales tax rate for this purchase?

Answer

Exercise  6.3.4 :

What is the sales tax rate if a $7,594 purchase will have $569.55 of sales tax added to it?

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step-by-step explanation: