# Question 7ddd4

Oct 5, 2017

These are linear equations, so identify your variables and equate them to each other to find the number of hours required to earn the same amount of money.

#### Explanation:

Both these scenarios are linear equations, meaning the variables have a degree of $1$.

Let's let $y =$ the total amount of money earned ($). Let's let $x =$the amount of time Tom spent working (in hours). The first plan describes a flat rate of $15, meaning there are no variables affecting the term. We can label this term as the constant.

On the other hand, it describes an hourly wage of ($4.50). Meaning this term is affected by a variable. Put this all together and we get an equation of $y = 4.50 x + 15$. The second plan describes just an hourly wage of $14.50#. There is no constant present, giving us the equation of $y = 14.50 x$.

Now it asks for how many hours must be worked for Britanny (You mean Tom?) in order to earn an equal amount of money for each plan.

If he is earning money with one plan and the same amount in the other, we can have each equation equal each other.

$4.50 x + 15 = 14.50 x$

Now we just isolate and solve for $x$.

$15 = 14.50 x - 4.50 x$

$15 = 10.00 x$

$1.5 = x$

Therefore, Tom has to work $1.5$ hours in each plan to earn an equal amount of money.

Another option to find the amount of hours, is to graph the equations and find the intersection.

Hope this helps :)

P.S. I don't who Brittany is...