Questions and Answers
Literal equations must have more than one variable.
True
Because unit multipliers have different expressions representing the same quantity in the numerator and denominator, their value is one.
True
A statement of equality between two ratios is called a __________.
proportion
All _________ are similar.
Signup and view all the answers
Convert 66 ft/sec to miles per hour. (1 mi = 5280 ft)
Signup and view all the answers
What is the unit rate if a car burns 150 gal on a 3000 mi trip?
Signup and view all the answers
Solve for d: 2d + 3/5 = 3d - 6/8.
Signup and view all the answers
Solve for m: 5 = (2m - b)/(m + b).
Signup and view all the answers
What percent of 65 is 52?
Signup and view all the answers
45% of what number is 225?
Signup and view all the answers
Find w. The figures are similar.
Signup and view all the answers
If the front face of the smaller figure has an area of 80, what is the area of the corresponding face of the larger figure? The two figures are similar.
Signup and view all the answers
If the volume of the larger figure is 3000, what is the volume of the smaller figure?
Signup and view all the answers
If the difference between Green Bay, Wisconsin, and Spokane, Washington, is 1650 mi, and on a map the distance is 25 in., what is the scale of the map?
Signup and view all the answers
Gabriela was given a 15% increase in wages. If she earned $36,000 last year, what can she expect to earn this year?
Signup and view all the answers
The density of a particular brand of corn syrup is known to be 1360 g/L. If Ai-Lin determined the density to be 1372 g/L, then what is the percent error of Ai-Lin's experiment?
Signup and view all the answers
What is the markup of a suit that costs a retailer $182 if he uses a standard markup rate of 30%?
Signup and view all the answers
What is the retail price of a suit that costs a retailer $182 if he uses a standard markup rate of 30%?
Signup and view all the answers
A retailer marks up all merchandise 50%. If a pair of basketball shoes costs the retailer $100, how much will they cost a shopper if he finds the shoes on a discount rack that advertises all shoes on the rack to be 50% off retail price?
Signup and view all the answers
A local steakhouse advertises a dinner special for $10. What will the total price of the special be after paying 12% sales tax and tipping 15% on the total bill?
Signup and view all the answers
A car salesman earns $500 per week plus 1.5% commission on his sales. If he sold two cars for a total of $55,000 last week, how much did he make?
Signup and view all the answers
Grandma has $250,000 to invest. She divides her money into two accounts. One account is in ultra-safe treasury bills paying 4% interest, and the other is in riskier corporate bonds paying 6%. If she needs $12,000 per year in income from her investments, how much should she invest in each account?
Signup and view all the answers
Steve bicycles 3 mi to school every day at 15 mi/hr. If school starts at 8:30 AM and he needs 15 min to lock his bike and get to his desk, then what time should he leave his house?
Signup and view all the answers
The distance from Cleveland to Chicago is 345 mi. A train, traveling at 45 mi/hr leaves Chicago heading to Cleveland at the same time that another train, traveling 30 mi/hr, leaves Cleveland heading to Chicago. How far from Chicago will the two trains meet?
Signup and view all the answers
How many gallons of ethanol are in a 100 gal mixture that is 10% ethanol?
Signup and view all the answers
If Holstein cows produce milk that is on average 3.66% butterfat and Jersey cows produce milk that is on average 4.5% butterfat, how many gallons of Jersey milk should be added to every 100 gal of Holstein milk to have milk that is 4% butterfat? Round your answer to the nearest tenth if needed.
Signup and view all the answers
Study Notes
Algebra Concepts and Definitions
- Literal equations include multiple variables, allowing for representation of relationships and conditions.
- Unit multipliers equate to one, enabling conversions through different expressions of the same quantity.
Ratios and Proportions
- Proportions involve a statement of equality between two ratios, crucial in solving algebraic equations.
- All squares share similarity in shape and angles, inherently making them similar figures.
Unit Conversions and Rates
- To convert 66 ft/sec to miles per hour yields a result of 45 mi/hr, highlighting the necessity of unit conversions in practical calculations.
- A car that burns 150 gallons over a trip of 3000 miles achieves a unit rate of 20 mi/gal, which effectively measures fuel efficiency.
Algebraic Equations
- The equation 2d + 3/5 = 3d - 6/8 resolves to d = -54, exhibiting the method of isolating variables to achieve solutions.
- To solve for m in the equation 5 = 2m - b/m + b, the result is m = -2b, exemplifying rearranging terms.
Percentage Calculations
- To determine what percent 52 is of 65, the answer is 80%, illustrating the process of calculating percentage of a whole.
- If 45% of an unknown number equals 225, the number is found to be 500, demonstrating reverse percentage calculation.
Similar Figures and Areas
- In similar figures, if the front face area of the smaller figure is 80, the corresponding area of the larger figure is 500, showcasing how similarity affects area.
- Volume relationships indicate if a larger figure has a volume of 3000, the smaller figure's volume would be 192, emphasizing proportionality in three dimensions.
Maps and Scales
- For map distances, if Green Bay and Spokane are 1650 miles apart with a distance of 25 inches on a map, the scale converts to 66 mi/in, critical for understanding real-world applications.
Financial Mathematics
- A 15% increase on a salary of $36,000 results in expected earnings of $41,400, illustrating salary growth.
- The density experiment shows a percent error of about 0.88%, demonstrating accuracy in measurements.
Retail Markups
- For a suit costing a retailer $182 with a 30% markup, the markup is $54.60, totaling a retail price of $236.60.
- A retailer applying a 50% markup on $100 basketball shoes results in a price of $150, but if discounted by 50%, shoppers pay $75.
Total Costs and Earnings
- A $10 dinner special incurs a total cost of $12.88 after a 12% sales tax and a 15% tip, emphasizing the total cost calculation process.
- A car salesman earns $1325 weekly from combined base pay and commission, demonstrating income structure in sales roles.
Investment Strategies
- Grandma's investment strategy involves $150,000 in treasury bills and $100,000 in corporate bonds to meet an annual income of $12,000, highlighting diversification.
Time and Travel Problems
- Steve needs to leave for school at 8:03 AM after accounting for commute time and preparations, showcasing time management in schedule planning.
- Train travel scenario shows convergence, with two trains meeting 207 miles from Chicago, illustrating relative motion and distance calculations.
Mixtures and Ratios
- A 100-gallon mixture with 10% ethanol contains 10 gallons of ethanol, demonstrating mixture calculations.
- To achieve 4% butterfat from Holstein and Jersey milk, adding 68 gallons of Jersey milk to every 100 gallons of Holstein is necessary, showcasing proportions in mixtures.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards covering key concepts from Algebra 1 Chapter 3. This quiz includes definitions and true/false statements about literal equations, unit multipliers, proportions, and similarities. Perfect for reviewing before a test or reinforcing your understanding of algebraic concepts.
