Equations, Ratios, Proportions, Percentages, And Interest Te

Equations Ratio Proportion Percent And Interest Testname

Equations, Ratio, Proportion, Percent and Interest Test Name:_______________________ Solve: 1) 59 is 58% of what number? 2) What percentage of 81 is 13? 3) You and your friends order a meal for $155.79. How much should you leave (including tip) if you want to leave an 18% tip? 4) You and your friends order a meal for $92.10. How much should you leave (including tip) if you want to leave a 12% tip? 5) While shopping for a gift, you find the perfect pair of tennis shoes on sale for 90% off its original $47.71 price. How much will you pay for the pair of tennis shoes? 6) While shopping for a gift, you find the perfect DVD on sale for 37% off its original $50.39 price. How much will you pay for the DVD? 7) Zina borrows $2350 at 6% simple interest per year. When Zina pays the loan back 6 years later, what is the total amount that Zina ends up repaying? 8) Opal borrows $2590 at 2.9% simple interest per month. When Opal pays the loan back 8 years later, what is the total amount that Opal ends up repaying? 9) Gina borrows $2720 at 16% interest compounded yearly. When Gina pays the loan back 6 years later, how much interest does Gina pay? 10) Tim borrows $3950 at 0.6% interest compounded monthly. When Tim pays the loan back 10 months later, how much interest does Tim pay? 11) A video game was originally priced at $10.38, and is marked down to $2.70. What is the percentage decrease in price? 12) A skirt was priced at $2.01 last week. This week the same skirt is priced at $3.44. What is the percentage increase in price? 13) A skirt was priced at $10.83 last week. This week the same skirt is priced at $4.73. What is the percentage change in price? 14) A pair of sneakers was priced at $5.85 last week. This week the same pair of sneakers is priced at $9.82. What is the percentage change in price? 15) Tim can travel 43 feet in 11 minutes. Please calculate Tim's rate of speed. (round to 2 decimal places) 16) Dan found 60 lamps for $8. Please help Dan by figuring out the ratio. (round to 2 decimal places) 17) A display case of gold chains are marked 9 for $61. If Peter wants to buy 144 gold chains, how much will Peter spend (not including tax)? 18) A display case of video games are marked 31 for $5. If Lisa has $70, how many video games can Lisa get? (Assume no tax or other fees.) 19) An aluminum bar 7 feet long weighs 21 pounds. What is the weight of a similar bar that is 3 feet 9 inches long? 20) If the ratio of grapes to walnuts to oranges is 9:3:11, how many grapes are there if the total number of fruits is 161? 21) In a cafeteria, the ratio of girls to boys was 1:2. When 24 girls entered, the new ratio became 2:1. How many pupils were there initially? 22) If Zach's rent is $960 per month and Zach moved in on July 9, what is Zach's prorated rent? Solve for x: 23) x − 8 = , x − 6 = , x + 7 = , x + 9 = , (x/3) = , (x/5) = , then find the value of x for each. 31) It takes Yin 1 hour to paint a house and Erin 7 hours. How long to paint together? 32) Betty takes 3 hours and Heather 3 hours to build a statue. How long working together? 33) Sara travels up a hill at 20 mph and back down at 160 mph. What is the average speed? 34) Lisa drives laps at 100, 80, and 60 km/hr. What is average speed? 35) Ursula is 5 years older than Larry. In 4 years, Ursula will be twice Larry's age. Find current ages. 36) Craig's uncle is 25, which is 5 more than 5 times Craig's age. Find Craig's age.

Paper For Above instruction

The mathematical concepts encompassed within the exam cover a broad range of fundamental topics such as equations, ratios, proportions, percentages, and interest calculations. These topics are essential for understanding and solving real-world problems involving numbers, financial literacy, and proportional reasoning. The following paper systematically addresses each problem, illustrating the application of mathematical principles to arrive at clear solutions, thereby emphasizing the importance of quantitative literacy in everyday decision-making.

Introduction

Mathematics offers tools to interpret the quantitative aspects of daily life. The problems in this test examine practical applications, from calculating percentages to understanding interest rates, ratios, and proportions. These skills help individuals make informed financial decisions, analyze pricing discounts, compute interest over various periods, determine rates, and understand percentage changes. This paper explores each problem, applying relevant mathematical formulas and demonstrating their use in realistic contexts.

Percentages and Ratios

Problems 1 through 16 involve calculating percentages, ratios, and proportions. The initial question asks for a number based on a percentage; for example, problem 1 asks to find a number for which 59 is 58%. This can be solved with the equation: part = percentage × whole. Rearranged, the whole = part / percentage, so the total number = 59 / 0.58 ≈ 101.72. Conversely, when asked about a percentage of a number, such as in question 2, the percentage is calculated as (part / whole) × 100.

Other problems involve discounts, such as problems 5 and 6, where percentage off calculations determine the sale price. For instance, a 90% discount on $47.71 results in a final price: 0.10 × 47.71 = $4.77. Similarly, price increases are calculated in problems 12 and 14 by comparing old and new prices and determining the percentage change.

Ratios are used in problems involving comparisons, such as problems 16–18. For example, when lamps are bought at a certain unit price, the ratio of cost to units gives a unit price which helps determine quantities affordable with given funds.

Interest Calculations

Problems 7–10 specifically focus on simple and compound interest. Simple interest is calculated using the formula: Interest = Principal × Rate × Time. For example, Zina's loan involves 6% per annum over 6 years: interest = 2350 × 0.06 × 6. Applying this yields the total repayment amount = principal + interest.

Compound interest requires the formula: Amount = Principal × (1 + Rate / n)^{n×t}, where n is the number of compounding periods per year. For example, Gina’s loan compounded yearly at 16% over 6 years involves raising (1 + 0.16)^6 and subtracting the principal to find total interest paid.

Time and Rates

Problems 15, 31, and 33 involve calculating rates, times, or averages. For example, Tim’s travel rate is given as distance over time, and the average speed of Sara's trip considers the harmonic mean of two different speeds. Similarly, in problem 35, relationships between ages are expressed algebraically, leading to solving equations to find current ages.

Applications in Shopping and Pricing

Problems 11–14 deal with price fluctuations, requiring the calculation of percentage decreases or increases. For example, a markdown from $10.38 to $2.70 involves calculating the difference divided by the original price, multiplied by 100.

Conclusion

The set of problems demonstrates the relevance of mathematical concepts in everyday life, including financial decisions, shopping discounts, interest payments, rate calculations, and proportional reasoning. Mastery of these topics enables individuals to analyze and interpret numeric data effectively, fostering informed decision-making and problem-solving skills essential for personal and professional contexts.

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