Math Problem Statement
Fred is 4 times as old as Nathan and is also 27 years older than Nathan. Let f be Fred's age and let n be Nathan's age. Which system of equations represents this situation?
Solution
The problem states:
- Fred is 4 times as old as Nathan.
- Fred is also 27 years older than Nathan.
We are asked to identify the correct system of equations, where:
- = Fred's age
- = Nathan's age
Translating the statements into equations:
-
"Fred is 4 times as old as Nathan" gives:
-
"Fred is 27 years older than Nathan" gives:
Checking Option A:
Option A provides the following system of equations:
n = 4f \\ n = f + 27 \end{cases}$$ - In the first equation, **$$n = 4f$$** is **incorrect** since the problem says Fred ($$f$$) is 4 times Nathan ($$n$$), not the other way around. - The second equation $$n = f + 27$$ is also **incorrect** because it suggests Nathan is older than Fred by 27 years, which is not true. Thus, **Option A is not correct**. --- The correct system of equations should be: $$\begin{cases} f = 4n \\ f = n + 27 \end{cases}$$ --- ### Final Note: Let me know if you'd like me to solve for Fred's and Nathan's ages, or if you have any additional questions! --- ### Related Questions: 1. How can you solve a system of two linear equations algebraically? 2. What are the methods for solving systems of equations (e.g., substitution, elimination)? 3. What happens when a system of equations has no solution? 4. Can you graph these equations to find the intersection point? 5. How can you verify the solution of a system of equations? --- ### Tip: Always carefully identify the relationships in word problems and assign variables logically before forming equations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Algebra
Formulas
f = 4n
f = n + 27
Theorems
Linear Equation Relationships
Suitable Grade Level
Grades 6-8