Chapter 1.1, Problem 16PPS

To determine

To evaluate: the given expression.

Answer to Problem 16PPS

  $3y+x-4z=10\frac{7}{15}$

Explanation of Solution

Given information:

Given expression

  $3y+x-4z$

And

  $w=-3,x=4,y=2.6$ , and $z=\frac{1}{3}$ .

Calculation:

Consider the given expression.

  $3y+x-4z$

Substitute the value of $x,y$ and $z$ in the given expression,

  $\begin{array}{c}3y+x-4z=3\left(2.6\right)+4-4\left(\frac{1}{3}\right)\\ =7.8+4-\frac{4}{3}\\ =\frac{78}{10}+4-\frac{4}{3}\\ =\frac{78\times 3+4\times 30-4\times 10}{30}\\ =\frac{234+120-40}{30}\\ =\frac{314}{30}\end{array}$

Now, convert the improper fraction into a mixed fraction.

  $\begin{array}{c}3y+x-4z=\frac{314}{30}\\ =\frac{30\times 10+14}{30}\\ =10\frac{14}{30}\\ =10\frac{7}{15}\end{array}$

Hence, the value of the expression is $10\frac{7}{15}$ .