Question

Katie is starting a babysitters sitting business. She spent $26 to make signs to advertise. She charges her initial fee of five dollars and then three dollars for each hour of service right in Solve inequality to find the number of hours she want to babysit to make a profit interpret the solution any quality

Answer 1

The Inequality representing the number of hours she want to babysit to make a profit is
`5+3x>26`.

Katie should babysit for more than 7 hours in order to make profit.

Explanation:

Given:

Money spent on advertising = $26

Initial fee = $5

Hourly charge = $3

We need to find the number of hours she want to babysit to make a profit.

Solution:

Let the number of hours be 'x'.

Now we can say that;

The sum of Initial fee and Hourly charge multiplied by number of hours should be greater than Money spent on advertising .

framing in equation form we get;

`5+3x>26`

Hence The Inequality representing the number of hours she want to babysit to make a profit is
`5+3x>26`.

On Solving the above Inequality we get;

Now Using Subtraction property of Inequality we will subtract both side by 5 we get;

`5+3x-5>26-5\\\\3x>21`

Now Using Division Property of Inequality we will divide both side by 3 we get;

`(3x)/(3)>(21)/(3)\\\\x>7`

Hence Katie should babysit for more than 7 hours in order to make profit.

Interpretation:

when x=7

Amount earned will be =
`5+3x=5+3*7 =5+21=\$26`

Profit earned will be = Amount earned - Money spent on advertising = 26 -26 =0

when x= 8

Amount earned will be =
`5+3x=5+3*8 =5+24=\$29`

Profit earned will be = Amount earned - Money spent on advertising = 29 -26 =$3

Hence at 7 hours of babysitting profit will be 0 and at 8 hours of babysitting profit will be $3.