Question

Whitney needs to paint her house so that she can sell it. She can choose between two different painters, George and Henry. George will charge $90 for the paint, and then $40 per hour. Henry will charge $120 for the paint and then $35 per hour. How long would both painters have to paint in order to charge Whitney the same amount? How much would her bill be?

Answer 1

Charges of George and Henry would be same if they paint for 6 hours.

For 6 hours of work both the charges of Painter George and Henry would be same which is $330.

Explanation:

Let the 'x' represents number of hours for work.

Also Let the 'y' represent the Total charge.

For Painter George:

Given:

Fixed charge = $90

Charge for each hour = $40

Amount of total charge is the sum of fixed charge and charge for each hour multiplied number of hours for work.

framing in equation form, we get;

`y= 90+40x \ \ \ \ equation\ 1`

For Painter Henry:

Given:

Fixed charge = $120

Charge of labor for each hour = $35

Amount of total charge is the sum of fixed charge and charge for each hour multiplied number of hours of work.

framing in equation form, we get;

`y =120+35x \ \ \ \ equation \ 2`

Now to find the number of hours painter will work in order that they would charge the same, we will make both the equation equal we get;

`90+40x=120+35x`

Now we solve the equation,

Combining the like terms, we get;

`40x-35x=120-90\\\\5x=30`

Dividing both side by '5' using division property, we get;

`(5x)/(5)= (30)/(5)\\\\x=6\ hrs`

Hence Charges of George and Henry would be same if they paint for 6 hours.

Charges of George after 6 hr =
`y=90+40x =90 +40* 6 = 90 +240 = \$330`

Charges of Henry after 6 hr =
`y=120+35x =120 +35* 6 = 120 +210 = \$330`

Hence For 6 hours of work both the charges of Painter George and Henry would be same which is $330.