 Math »
 Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late..?
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late..?
Discover the cost of tardiness with library books  every overdue day incurs a $0.30 fee. Explore viable solutions with our ordered pair calculator.
by Maivizhi A
Updated Mar 18, 2024
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?
A. (–3, –0.90)
B. (–2.5, –0.75)
C. (4.5, 1.35)
D. (8, 2.40)
Answer:
Given the conditions, we can eliminate the ordered pairs with negative xvalues since they represent scenarios where the book is returned early, not late. Therefore, we can disregard (–3, –0.90) and (–2.5, –0.75).
Regarding the ordered pair (4.5, 1.35), it's important to note that the fee is charged at midnight, so if the book is 4.5 days late, it incurs the fee for 4 days late, not 5 days. Therefore, the fee for 4.5 days late would be the same as for 4 days late, which is $1.20, not $1.35. Thus, (4.5, 1.35) is not a valid solution.
Finally, for (8, 2.40), when the book is 8 days late, the total fee would be 8×0.30=2.40, which matches the given yvalue in the ordered pair. Therefore, (8, 2.40) is indeed the correct solution.
Linear Equations and their Applications
Linear equations are mathematical expressions that describe relationships between variables where each term is either a constant or a product of a constant and a variable raised to the first power. They take the form: ax + by = c. Where a, b, and c are constants, and x and y are variables. Linear equations are fundamental in mathematics and have various applications across different fields:

Physics: Linear equations are commonly used in physics to describe relationships between physical quantities. For example, the equation F = ma, which describes Newton's second law of motion, is a linear equation where F is force, m is mass, and a is acceleration.

Engineering: Engineers use linear equations extensively in designing structures, analyzing circuits, and solving optimization problems. Linear equations help in modeling various systems and understanding their behavior.

Economics: Linear equations are used in economic models to represent relationships between variables such as supply and demand, cost and revenue, or investment and return. These models help economists make predictions and decisions about economic phenomena.

Finance: Linear equations are used in finance to calculate interest rates, determine loan payments, and analyze investment portfolios. They are also used in risk assessment and financial planning.

Computer Graphics: In computer graphics, linear equations are used to represent lines and other geometric shapes. Algorithms based on linear equations are used to render images, create animations, and simulate 3D environments.

Statistics: Linear regression, a statistical technique used to model the relationship between two or more variables, is based on linear equations. It is widely used in data analysis, prediction, and hypothesis testing.

Chemistry: Linear equations are used in chemical reactions to balance equations and calculate quantities of reactants and products. They are also used in spectroscopy and other analytical techniques.

Operations Research: Linear programming, a method used to optimize the allocation of resources, is based on linear equations. It is used in various industries, such as manufacturing, transportation, and logistics, to improve efficiency and reduce costs.
These are just a few examples of how linear equations are applied in different fields. Their simplicity and versatility make them indispensable tools for modeling realworld phenomena and solving practical problems.
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee FAQs
1. What is a linear equation?
A linear equation is a mathematical expression that describes a relationship between variables where each term is either a constant or a product of a constant and a variable raised to the first power.
2. What is the general form of a linear equation?
The general form of a linear equation is ax + by = c, where a, b, and c are constants, and x and y are variables.
3. How are linear equations used in physics?
Linear equations are used in physics to describe relationships between physical quantities. For example, Newton's second law of motion, F = ma, is a linear equation where F is force, m is mass, and a is acceleration.
Recent Updates
 Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevati...
 Aman’s salary is first increased by 25% and then decreased by 20%. The result is the ...
 P and S can complete a piece of work in 20 and 15 days respectively. They worked togeth...
 A boatman can row 2 km against the stream in 20 minutes and return in 10 minutes. Find ...
 The numbers 33, 45 and 78, used in relation to vinyl records, refer to how much they co...
 The angle between the minute hand and the hour hand of a clock when the time is 7 : 20 ...
 A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 bal...
 In a group of 6 boys and 4 girls, Four children are to be selected. In how many differe...
 What are the Parts of circle?
 The compound interest on a certain sum of money for 2 years at 10 % per annum is Rs 420...
 Simple interest on a sum of money for 2 years at 4 % is rupees 450. Find compound int...
 Simplify (ab^2 c^3) * (a^4 b^5 c^6) / (a^7 b^8 c^9) * (a^10 b^11 c^12) * (a^13 b^1...
 A machine can print 12 page in a minute. How long will the machine take to print 5760 p...
 There are 20 points in a plane, how many triangles can be formed by these points if 5 a...
 The total cost of chocolates purchased by Sabu is ₹68.25. If the cost of one chocolat...