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Chapter 5: Problem 12

Leslie placed this ad in the Collector Car Monthly. 1957 Chevrolet Nomad station wagon. Tropical Turquoise, 6 cyl. auto, PS, PW AM/FM, repainted, rebuilt transmission, restored two-tone interior. Mint! Moving, sacrifice, \(\$ 52,900.555-4231\) a. If the newspaper charges \(\$ 48\) for the first three lines and \(\$ 5\) for each extra line, how much will this ad cost Leslie? b. Ruth buys the car for 8\(\%\) less than the advertised price. How much does she pay? Ruth must pay her state 6\(\%\) sales tax on the sale. How much must she pay in sales tax? c. Ruth must pay her state 6\(\%\) sales tax on the sale. How much must she pay in sales tax?

Short Answer

Expert verified
a. The ad will cost Leslie \( $ 63 \). b. Ruth pays \( $ 48,668 \) for the car. c. Ruth must pay \( $ 2,920.08 \) in sales tax.

Step by step solution

01

Calculate the Cost of the Ad

The ad consists of six lines. The newspaper charges \( $ 48 \) for the first three lines and \( $ 5 \) for each additional line. Calculate the cost for the extra lines and add this to the cost for the first three lines.
02

Calculate the Price After Discount

The advertised price for the car is \( $ 52,900 \). Ruth buys the car for 8% less than this price. Calculate 8% of the advertised price and subtract it from the original price to find the discounted price Ruth pays.
03

Calculate the Sales Tax

Ruth must also pay a 6% sales tax on her purchase. Calculate 6% of the discounted price Ruth pays to find out how much she must pay in sales tax.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Advertising Costs
When placing an ad in a newspaper, understanding how the costs accumulate is essential. Leslie's advertisement example helps illustrate these calculations. The advertised cost includes a base fee plus additional costs for exceeding a specific line limit.

For this ad, the first three lines are covered by a flat fee of $48. However, Leslie鈥檚 ad consists of six lines, meaning there are three extra lines. Each extra line is charged at $5. To find the total cost, we first calculate the cost for the additional lines:
  • Extra lines: 6 total lines - 3 included lines = 3 extra lines
  • Cost for extra lines = 3 lines x $5/line = $15
Next, add the base fee to the extra line cost:
  • Total ad cost = $48 + $15 = $63
So, Leslie's total advertising expense for the ad is $63.
Percentage Discount Calculation
Ruth manages to snag a deal on the advertised 1957 Chevrolet Nomad. Understanding percentage discounts helps determine how much Ruth actually pays. The advertised price is $52,900, and Ruth receives an 8% discount.

To calculate the discount, you determine 8% of the $52,900:
  • Discount amount = 8/100 x $52,900 = $4,232
Now subtract the discount from the original price to find out what Ruth pays:
  • Discounted price = $52,900 - $4,232 = $48,668
Thus, Ruth pays $48,668 for the car after the discount is applied.
Sales Tax Computation
After getting a discount, don't forget about the sales tax, which is an additional cost when buying goods and services. Ruth has to pay a 6% sales tax on her purchase of the Nomad.

First, calculate 6% of Ruth's discounted purchase price of $48,668:
  • Sales tax amount = 6/100 x $48,668 = $2,920.08
Add this sales tax to the discounted price to determine Ruth's total cost:
  • Total amount paid = $48,668 + $2,920.08 = $51,588.08
Therefore, the total amount Ruth has to pay, after accounting for sales tax, is $51,588.08.

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Most popular questions from this chapter

A local newspaper charges by the character for its classified ads. Letters, numbers, spaces, and punctuation each count as one character. They charge \(\$ 46\) for the first 200 characters and \(\$ 0.15\) for each additional character. a. If \(x\) represents the number of characters in the ad, express the cost \(c(x)\) of an ad as a piece wise function. b. Graph the function from part a. c. Find the coordinates of the cusp in the graph in part b.

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