Question

The function y = 10x + 100 represents the amount y (in dollars) of money in your bank account after you babysit for x hours.a.) If you babysit 4 hours, how much money will you earn?b.) If you have $210 in your bank account after one month, how many hours did you babysit for this month?

Answer 1

We will investigate how to use linear relations to determine the amount of earnings made from babysitting service.

The earnings ( y ) are expressed as a function of babysitting hours ( x ) as a linear function as follows:

`y\text{ = 10x + 100}`

a) We will use the above given linear model to determine the amount of money earned if one babysits for 4 hours.

We will declare the given variable:

`x\text{ = 4}`

The function variable ( y ) i.e the amount of earnings can be determined from the given linear equation:

`\begin{gathered} y\text{ = 10}\cdot(4)\text{ + 100} \\ y\text{ = 40 + 100} \\ y\text{ = 140} \end{gathered}`

The amount of money earned against 4 hours of babysitting is:

`\text{\$}140`

b) We will determine the number of hours off babysitting calendered for the month given that we have $210 in our bank.

We will declare the given variable:

`y\text{ = 210}`

The function variable ( y ) i.e the amount of earnings can be determined from the given linear equation:

`\begin{gathered} 210\text{ = 10}\cdot(x)\text{ + 100} \\ 110\text{ = 10}\cdot x \\ \\ x\text{ = }(110)/(10)\text{ } \\ \\ x\text{ = 11 }\ldots\text{ Answer} \end{gathered}`

The amount of hours accumulated for babysitting in this month is:

`11\text{ hours}`