Find the value of [tex]$y$[/tex] in the formula [tex]$y=5 a-3 b+c$[/tex], if [tex]$a=12, b=4$[/tex], and [tex]$c=8$[/tex].
A. 64
B. 80
C. 56
D. 40
Answer (2)
Substitute the given values a = 12 , b = 4 , and c = 8 into the formula y = 5 a − 3 b + c .
Calculate 5 × 12 = 60 and 3 × 4 = 12 .
Substitute these results back into the equation: y = 60 − 12 + 8 .
Simplify to find the value of y : y = 56 . Therefore, the final answer is 56 .
Explanation
Understanding the Problem We are given the formula y = 5 a − 3 b + c , and we are also given the values a = 12 , b = 4 , and c = 8 . Our goal is to find the value of y by substituting the given values into the formula.
Substituting the Values Now, let's substitute the given values into the formula: y = 5 ( 12 ) − 3 ( 4 ) + 8
Performing Multiplication Next, we perform the multiplication operations: y = 60 − 12 + 8
Performing Addition and Subtraction Now, we perform the addition and subtraction operations from left to right: y = 48 + 8 y = 56
Final Answer Therefore, the value of y is 56.
Examples
This type of problem is useful in various real-life scenarios. For example, imagine you are calculating the total cost of a project. You have a fixed cost per item ( a ), a discount per item ( b ), and an additional one-time cost ( c ). The formula helps you determine the total cost ( y ) based on these factors. Understanding how to substitute values into a formula and simplify the expression is a fundamental skill in many practical applications, such as budgeting, engineering, and finance.
The value of y in the formula y = 5 a − 3 b + c with the given values is 56. After substituting and simplifying the equation, we find that the answer is 56 .
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