Questions and Answers
If a car averages 27 miles per gallon and gas costs $4.04 per gallon, how much would the gas cost for the car to travel 2,727 miles?
When x = 3 and y = 5, by how much does the value of 3x² - 2y exceed the value of 2x² - 3y?
14
What is the value of x when 2x + 3 = 3x - 4?
7
What is the greatest common factor of 42, 126, and 210?
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If the third year's sales were 38 million dollars and they were double the sales of the second year, what were the first year's sales in millions?
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If pumping a mine that is 150 feet deep requires a pump that pumps a minimum of how many gallons per minute?
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How many irrational numbers are there between 1 and 6?
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What is the maximum number of pounds of sugar to be consumed by each track team member in the coming year if they plan to lower their sugar intake by 20%?
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If the lead of a screw is 1/8 inch, how many complete turns would it take to advance it 2.5 inches in total?
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If xy = 144, x + y = 30, and x > y, what is the value of x - y?
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What is the answer to the last question in the exercise?
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Study Notes
Gas Cost Calculation
- To determine gas costs, divide total miles by miles per gallon: 2,727 miles ÷ 27 mpg = 101 gallons.
- Multiply gallons by gas price: 101 × $4.04 = $408.04, indicating total gas cost for travel.
Expression Evaluation
- Given values x = 3 and y = 5, calculate expressions:
- 3x² - 2y → 3(3)² - 2(5) = 27 - 10 = 17
- 2x² - 3y → 2(3)² - 3(5) = 18 - 15 = 3
- The difference: 17 - 3 = 14 indicates how much one expression exceeds the other.
Simple Equation Solving
- Solve for x in the equation:
- Start with 2x + 3 = 3x - 4
- Rearrange to x - 4 = 3, leading to x = 7.
Greatest Common Factor
- Factor 42, 126, and 210:
- 42 = 2 × 3 × 7
- 126 = 2 × 3² × 7
- 210 = 2 × 3 × 5 × 7
- The greatest common factor is 2 × 3 × 7 = 42.
Sales Growth Calculation
- Define sales: first year = x, second year = x + 3, third year = 2(x + 3).
- Given the third-year sales as 38 million: 2(x + 3) = 38 leads to first-year sales of x = 16 million after solving.
Pump Capacity for Mines
- Pumping requirement based on mine depth (D feet):
- Given D = 150: the pump must pump (+ 4D - 250) gallons per minute.
- Substituting gives: + 4(150) - 250 = 350 gallons per minute.
Irrational Numbers
- Between any two real numbers, such as 1 and 6, there are infinitely many irrational numbers.
Sugar Consumption Reduction
- A typical high school student consumes 67.5 pounds of sugar yearly.
- Track team members aim to reduce consumption by 20%, i.e., they will consume 80% of 67.5, yielding 54 pounds as a maximum for each member.
Screw Turns Calculation
- Each turn of the screw advances 1/8 inch; the screw is 2 ½ inches long.
- To find turns to embed the screw, use: (Total length of screw ÷ Lead per turn), resulting in 20 complete turns.
Problem Solving with Quadratic Equations
- Given xy = 144 and x + y = 30 with the condition x > y.
- Substitute to convert into a quadratic equation: (x² - 30x + 144 = 0).
- Solutions yield x = 24 and y = 6 leading to x - y = 18.
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Description
Test your ACT math skills with these flashcards that cover various types of problems. This set focuses on real-world applications of math concepts, such as calculating gas costs based on mileage and fuel prices. Perfect for ACT test preparation and mastering practical math calculations.
