What is the value of $x$ in the equation $3x - 4y = 65$, when $y = 4$?
A. $x=13 \frac{1}{4}$
B. $x=21 \frac{2}{3}$
C. $x=23$
D. $x=27
Answer (1)
Substitute the given value of y into the equation.
Simplify the equation by performing the multiplication.
Isolate the term with x by adding to both sides.
Solve for x by dividing both sides by its coefficient.
The value of x is 27 .
Explanation
Problem Setup We are given the equation 3 x − 4 y = 65 and the value y = 4 . Our goal is to find the value of x .
Substitution Substitute y = 4 into the equation: 3 x − 4 ( 4 ) = 65
Simplification Simplify the equation: 3 x − 16 = 65
Isolating the x term Add 16 to both sides of the equation: 3 x = 65 + 16
Further Simplification Calculate the sum: 3 x = 81
Solving for x Divide both sides by 3 to solve for x : x = 3 81
Final Calculation Calculate the value of x : x = 27
Examples
Imagine you're buying tickets for a concert. The total cost is determined by a fixed service fee and the number of tickets you purchase. If the service fee is $4 per ticket and the total bill is $65 for 3 tickets, you can use this type of equation to find the price of each ticket. This problem demonstrates how linear equations can model real-world scenarios involving costs and quantities. Understanding how to solve for variables in such equations helps in budgeting and making informed purchasing decisions.
