Chapter 4.1, Problem 3GP

To determine

To Calculate:

The linear equation to find Ethan’s total weekly pay T if he makes d deliveries.

Answer to Problem 3GP

Linear equation find Ethan’s total weekly pay T if he makes d deliveries :

  $T=16d+135$

Explanation of Solution

Given Information:

In addition to the weekly salary, Ethan is paid $16 per delivery.Last week , he made 5 deliveries and his total pay was $215.

Let

T = Total pay of Ethan per week = $215

d = Number of deliveries in a week = 5

b = The weekly salary of Ethan

m = Pay per delivery = $16

Formula Used:

Equation of slope-intercept form of a line is given by:

  $y=mx+b\mathrm{............................}(1)$

Where

  $\begin{array}{l}b=y-\mathrm{int}ercept\\ m=\frac{rise}{run}=slope\end{array}$

Calculation:

First , we form the equation :

Let

T = Total pay of Ethan per week = $215

d = Number of deliveries in a week = 5

b = The weekly salary of Ethan

m = Pay per delivery = $16

Now, we form the equation :

Pay per delivery = $16

So, pay of d deliveries in a week = 16d

The salary of Ethan per week = b

So, the linear equation ( slope-intercept form) of Ethan’s total weekly pay T if he makes d deliveries

  $T=16d+b\mathrm{..............................}(2)$

Now , we find b by substituting the values in (2)

  $\begin{array}{l}T=215\\ d=5\\ T=16d+b\mathrm{..........................................}[T=215,d=5]\\ \Rightarrow 215=16\cdot 5+b\mathrm{................................}[substituting]\\ \Rightarrow 215=80+b\mathrm{..................................}[simplify]\\ \Rightarrow 275-80=80+b-\mathrm{80...............}[subtract"80"each\_side]\\ \Rightarrow 135=b\mathrm{..............................................}[simplify]\\ or\\ b=135\end{array}$

Hence, the weekly salary of Ethan = $135.

Substituting the value in equation (2)

  $\begin{array}{l}b=135\\ T=16d+b\mathrm{...........................}(1)\\ \Rightarrow T=16d+\mathrm{135.....................}[b=135]\end{array}$

The required equation of Ethan’s total weekly pay T if he makes d deliveries

  $T=16d+135$