Question

if Rachel works as tutor for $7 an hour and as a waitress for $13 am hour. this month she worked a combined total of 105 hours at two jobs. let t be the number of hours Rachel worked as a tutor this month write an expression for the combined total dollar amount she earned this month?

Answer 1

Solution:

The number of hours worked for the month is

$=105$

The amount earned as a tutor for one hour is

$=7$

The amount earned as a waitress for one hour is

$=13$

The number of hours Rachel worked as a tutor is

$=t$

Let the number of hours she worked as a waitress be

$=x$

The equation representing the total hours worked for the month will be

$\begin{gathered} x+t=105 \\ x=105-t\ldots\ldots\text{.}(1) \end{gathered}$

The amount of money Rachel earned as a tutor this month will be calculated as

$\begin{gathered} =7\times t \\ =7t \end{gathered}$

The amount of money Rachel earned as a waitress this month will be calculated as

$\begin{gathered} =13\times x \\ =13x \end{gathered}$

The expression to represent the combined total earned this month will be

$=7t+13x\ldots\ldots\text{.}(2)$

Substitute equation (1) in equation (2) above, we will have

$\begin{gathered} x=105-t\ldots\ldots\text{.}(1) \\ =7t+13x\ldots\ldots\text{.(}2) \\ =7t+13(105-t) \\ =7t+1365-13t \\ =1365-6t \end{gathered}$

Hence,

The expression for the combined total she earned this month = 1365 -6t