Find the value of the expression $(4 x-12)+\left(\frac{1}{2} x y-10\right)$ for $x=4$ and $y=6$.
Answer (1)
Substitute x = 4 and y = 6 into the expression ( 4 x − 12 ) + ( 2 1 x y − 10 ) .
Calculate 4 ( 4 ) − 12 = 16 − 12 = 4 .
Calculate 2 1 ( 4 ) ( 6 ) − 10 = 12 − 10 = 2 .
Add the results: 4 + 2 = 6 .
Explanation
Understanding the Problem We are given the expression ( 4 x − 12 ) + ( 2 1 x y − 10 ) and we need to find its value when x = 4 and y = 6 .
Substituting the Values First, substitute the given values of x and y into the expression: ( 4 ( 4 ) − 12 ) + ( 2 1 ( 4 ) ( 6 ) − 10 ) .
Simplifying the First Parenthesis Now, simplify the expression by performing the arithmetic operations inside the parentheses. First, calculate 4 ( 4 ) − 12 : 4 ( 4 ) − 12 = 16 − 12 = 4 .
Simplifying the Second Parenthesis Next, calculate 2 1 ( 4 ) ( 6 ) − 10 : 2 1 ( 4 ) ( 6 ) − 10 = 2 1 ( 24 ) − 10 = 12 − 10 = 2 .
Adding the Results Finally, add the two results: 4 + 2 = 6 . Therefore, the value of the expression is 6.
Examples
Imagine you are calculating the total cost of materials for a project. You have a fixed cost component ( 4 x − 12 ) and a variable cost component that depends on the amount of materials used ( 2 1 x y − 10 ). If x represents the quantity of a primary material and y represents the quantity of a secondary material, this expression helps you determine the total cost by substituting the actual quantities used. For example, if x = 4 units and y = 6 units, the total cost would be $6. This kind of calculation is fundamental in project management and cost estimation.
