# Algebra Homework #28

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Questions: 8 | Attempts: 307

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Careful with UNITS! You must write in the \$ or %. Do not write words like points or students.

• 1.

### Olivia purchases a DVD movie priced at \$21.99. The sales tax is 6.5% total price of the movie, including tax?

Explanation
The total price of the movie, including tax, is \$23.42. This is calculated by adding the sales tax of 6.5% to the original price of \$21.99. To find the tax amount, we multiply \$21.99 by 6.5% (or 0.065), which equals \$1.43. Adding this tax amount to the original price gives us a total of \$23.42.

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• 2.

### The ACT is a college entrance exam taken by high school students. The maximum score that can be earned is 36. The average score in the United States was 21.2 during a recent year. The average score for Vermont students that year was 7.5% higher than the national average. What was the average ACT score for Vermont students? Round your answer to the nearest tenth.

Explanation
The average ACT score for Vermont students was 22.8. This can be calculated by adding 7.5% of the national average score (21.2) to the national average score. 7.5% of 21.2 is 1.59. Adding this to 21.2 gives us 22.79, which rounds to 22.8 when rounded to the nearest tenth.

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• 3.

### Mr. Thompson plans to purchase a used car priced at \$8400. He will receive a 15% employee discount and then will have to pay a 5.5% sales tax. What will be the final price of the car?

Explanation
Mr. Thompson plans to purchase a used car priced at \$8400. He will receive a 15% employee discount, which means he will pay only 85% of the original price. Therefore, the price after the discount is 8400 * 0.85 = \$7140. Then, he will have to pay a 5.5% sales tax on this discounted price. The sales tax amount is 7140 * 0.055 = \$392.70. Adding this tax to the discounted price gives us 7140 + 392.70 = \$7532.70, which is the final price of the car.

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• 4.

### The price per share of a stock decreased from \$90 per share to \$36 per share. By what percent did the price of the stock decrease?

Explanation
The price per share of the stock decreased from \$90 to \$36, which is a decrease of \$54. To find the percentage decrease, we divide the decrease (\$54) by the original price (\$90) and multiply by 100. This gives us a percentage decrease of 60%.

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• 5.

### Customers of a utility company received notices in their monthly bills that heating costs for the average customer had increased 125% over last year because of an unusually severe winter. In January of last year, the Garcia’s paid \$120 for heating. What should they expect to pay this January if their bill increased by 125%?

Explanation
The Garcia's should expect to pay \$270 this January if their bill increased by 125%. This can be calculated by adding 125% of \$120 to the original amount. 125% of \$120 is \$150, so \$120 + \$150 = \$270.

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• 6.

### A pair of Jordans cost \$255.00 (retro 12), but they were on sale for 30% off. The sales tax was 5.5%, what is the final price?

Explanation
The final price can be calculated by first determining the discounted price of the Jordans. To find the discounted price, we multiply the original price (\$255) by the discount percentage (30%) and subtract that amount from the original price. This gives us a discounted price of \$178.50. Next, we calculate the sales tax by multiplying the discounted price (\$178.50) by the sales tax rate (5.5%) and adding that amount to the discounted price. This gives us a final price of \$188.32.

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• 7.

### The original selling price of a new sports video was \$65.00. Due to the demand the price was increased to \$87.75. What was the percent of increase over the original price?

Explanation
The percent of increase over the original price can be calculated by finding the difference between the new price and the original price, dividing it by the original price, and then multiplying by 100. In this case, the difference between the new price (\$87.75) and the original price (\$65.00) is \$22.75. Dividing this by the original price and multiplying by 100 gives us a percent of increase of 35%.

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• 8.

### A high school paper increased its sales by 75% when it ran an issue featuring a contest to win a class party. Before the contest issue, 10% of the school’s 800 students bought the paper. How many students bought the contest issue?

Explanation
Before the contest issue, 10% of the 800 students bought the paper, which equals 80 students. If the paper increased its sales by 75%, then that means that 75% more than 80 students bought the paper, which means that 60 more people bought the paper than before. How many in total?

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• Mar 19, 2023
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• Oct 05, 2016
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