Solve the following expression:
[tex]
\begin{array}{c}
a=3 \text { and } c=5 \\
5 a+12-2 c+a
\end{array}
[/tex]
Answer (2)
Substitute the given values a = 3 and c = 5 into the expression 5 a + 12 − 2 c + a .
Simplify the expression by performing the multiplications: 5 ( 3 ) + 12 − 2 ( 5 ) + 3 = 15 + 12 − 10 + 3 .
Perform the addition and subtraction from left to right: 15 + 12 − 10 + 3 = 20 .
The final result of the expression is 20 .
Explanation
Understanding the Problem We are given the expression 5 a + 12 − 2 c + a and the values a = 3 and c = 5 . Our goal is to substitute these values into the expression and simplify to find the final result.
Substitution First, substitute the given values of a and c into the expression: 5 ( 3 ) + 12 − 2 ( 5 ) + 3
Multiplication Next, perform the multiplications: 15 + 12 − 10 + 3
Addition and Subtraction Now, perform the addition and subtraction from left to right: 15 + 12 = 27 27 − 10 = 17 17 + 3 = 20
Final Answer Therefore, the final result is 20.
Examples
This type of algebraic expression evaluation is useful in many real-world scenarios. For example, if you are calculating the total cost of items where 'a' represents the number of apples you buy and 'c' represents the number of oranges, the expression can help you determine the total cost, considering different prices and a fixed additional cost (like a delivery fee). Understanding how to substitute values and simplify expressions is fundamental in budgeting, financial planning, and even in basic physics calculations.
By substituting the values of a and c into the expression and simplifying step-by-step, we find that the final result is 20. This was achieved through substitution, multiplication, and performing the addition and subtraction in order. The expression evaluates to 20.
;
