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?

Answer:

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)

Simplify r = 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?

You can use the method of calculating the percentage of an amount to find out the discount amount.

The discount price for the given condition was $205.2

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is [tex]\dfrac{a}{100} \times b[/tex]

First we will find the marked price since the discount price was calculated on the marked price.

Since marked price was 150% of the cost price $456, thus,

[tex]\text{Marked price} = \dfrac{456}{100} \times 150 = \$684[/tex]

Thus, the marked price of the furniture was $684

Now, since the discount offered on the price was 30%, thus,

[tex]Discount = \dfrac{\text{Marked price}}{100} \times \text{Discount percent} =\dfrac{684}{100} \times 30\\\\Discount = \$205.2[/tex]

Thus,

The discount price for the given condition was $205.2

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