What is the value of $a$ in the equation $3a + b = 54$, when $b = 9$?
Answer (2)
Substitute the given value of b into the equation.
Simplify the equation by subtracting 9 from both sides.
Divide both sides by 3 to solve for a .
The value of a is 15 .
Explanation
Understanding the Problem We are given the equation 3 a + b = 54 and the value b = 9 . Our goal is to find the value of a .
Substituting the Value of b Substitute the value of b into the equation: 3 a + 9 = 54
Isolating the Term with a Subtract 9 from both sides of the equation to isolate the term with a : 3 a = 54 − 9 3 a = 45
Solving for a Divide both sides of the equation by 3 to solve for a : a = 3 45 a = 15
Final Answer Therefore, the value of a is 15.
Examples
Imagine you're planning a pizza party and need to figure out how many slices each person gets. If the total number of slices is represented by 3 a + b = 54 , where a is the number of slices per person and b is the leftover slices, and you know there are 9 leftover slices ( b = 9 ), you can use this equation to determine how many slices each person gets. Solving for a gives you the number of slices per person, ensuring everyone gets a fair share. This problem demonstrates how algebraic equations can help in everyday planning and resource allocation.
The value of a in the equation 3 a + b = 54 when b = 9 is 15 . This is found by substituting the value of b , isolating a , and solving the equation. The final answer is 15 .
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