Question

Julio is paid 1.1 times his normal hourly rate for each hour he works over 28 hours in a week. Last week he worked 35 hours and earned $496.23Enter and solve and equation to find Julio’s normal hourly rate, r. Complete the explanation how you know that your answer is reasonable.The earnings equation is $496.23 = _________Julio’s hourly rate is $ ______per hour.This is reasonable because working 35 hours at a rate of $14 per hour is 35 • 14 = 35(10+4) = 350 + 140 = _____And $______ is close to $496.23

Answer 1

The earnings equation is $496.23 = _35.7x_____

Julio’s hourly rate is $ __13.9____per hour.

This is reasonable because working 35 hours at a rate of $14 per hour is 35 • 14 = 35(10+4) = 350 + 140 = __490___

And $___490___ is close to $496.23

Explanation

Step 1

Let

x represents the normal hourly rate

if the numbers of worked hours is greater than 28 in a week

1.1 x= hourly rate

Step 2

Last week he worked 35 hours and earned $496.23

Hence

the number of hours he worked after 28 hours=35-28=7

the wage for those hours is

$\begin{gathered} \text{wage}1=7\cdot1.1x \\ \text{wage}1=7.7x \end{gathered}$

and, he worked 28 hours at a normal rate

$\begin{gathered} \text{wage 2= 28}\cdot1x \\ wage\text{2 =28x} \end{gathered}$

then, the total he earned is

$\begin{gathered} total\text{ = wage1 +wage 2} \\ \text{replacing} \\ 496.23=7.7x+28x \\ 496.23=35.7\text{ x} \end{gathered}$

Step 3

solve for x

$\begin{gathered} 496.23=35.7x \\ x=\frac{496.23}{35.7} \\ x=13.9 \end{gathered}$

Step 4

This is reasonable because working 35 hours at a rate of $14 per hour is 35 • 14 = 35(10+4) = 350 + 140 = __490___

And $___490___ is close to $496.23

I hope this helps you