Chapter 1.2, Problem 15WE

a.

To determine

To Evaluate: The expression $4xz+3y$ if $t=6$ , $x=3$ , $y=4$ , and $z=5$

Answer to Problem 15WE

The value of the expression $4xz+3y$ is $4xz+3y=72$

Explanation of Solution

Given information:

The expression $4xz+3y$ and the values $t=6$ , $x=3$ , $y=4$ , and $z=5$

Concept Used:

The value of an expression at the given values of the unknowns is calculated by substituting the given values of the unknowns into the expression and simplifying it.

Calculation:

Given the expression $4xz+3y$

Evaluating the expression $4xz+3y$ at $x=3$ , $y=4$ , and $z=5$ , we have

  $\begin{array}{c}4xz+3y=4\left(3\right)\left(5\right)+3\left(4\right)\text{ Substituting } x=3\text{, }y=4\text{, } z=5\\ =60+12\text{ Multiplying}\\ =72\text{ Adding}\end{array}$

Therefore, $4xz+3y=72$

Conclusion:

The value of the expression $4xz+3y$ is $4xz+3y=72$

b.

To determine

To Evaluate: The expression $4\left(xz+3y\right)$ if $t=6$ , $x=3$ ,

  $y=4$ , and $z=5$

Answer to Problem 15WE

The value of the expression $4\left(xz+3y\right)$ is $4\left(xz+3y\right)=108$

Explanation of Solution

Given information:

The expression $4\left(xz+3y\right)$ and the values $t=6$ ,

  $x=3$ , $y=4$ , and $z=5$

Concept Used:

The value of an expression at the given values of the unknowns is calculated by substituting the given values of the unknowns into the expression and simplifying it.

Calculation:

Given the expression $4\left(xz+3y\right)$

Evaluating the expression $4\left(xz+3y\right)$ at $x=3$ , $y=4$ , and $z=5$ , we have

  $\begin{array}{c}4\left(xz+3y\right)=4\left(\left(3\right)\left(5\right)+3\left(4\right)\right)\text{ Substituting } x=3\text{, }y=4\text{, } z=5\\ =4\left(15+12\right)\text{ Multiplying in bracket}\\ =4\left(27\right)\text{ Adding in bracket}\\ =108\text{ Multiplying}\end{array}$

Therefore, $4\left(xz+3y\right)=108$

Conclusion:

The value of the expression $4\left(xz+3y\right)$ is $4\left(xz+3y\right)=108$