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

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* t \\ =7t \end{gathered}`

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

`\begin{gathered} =13* 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