Math / Algebra

Question- The Smith family and the Jackson family are having their basements remodeled. The Smith's contractor charges $\$ 16.50$ per hour plus $\$ 289$ in supplies. The Jackson's contractor charges $\$ 18.75$ per hour and $\$ 274.60$ in supplies. At how many hours of work will the total cost be the same for both families?

Studdy Solution

STEP 1

1. The Smith family's contractor charges $16.50 per hour plus$ 289 in supplies.
2. The Jackson family's contractor charges $18.75 per hour plus$ 274.60 in supplies.
3. We want to find the number of hours at which the total cost for both families is the same.

STEP 2

1. Define variables for the number of hours.
2. Write expressions for the total cost for each family.
3. Set the expressions equal to each other to find the number of hours.
4. Solve the equation for the number of hours.

STEP 3

Define a variable for the number of hours of work. Let $h$ represent the number of hours.

STEP 4

Write expressions for the total cost for each family.
For the Smith family, the total cost is: $C_{\text{Smith}} = 16.50h + 289$
For the Jackson family, the total cost is: $C_{\text{Jackson}} = 18.75h + 274.60$

STEP 5

Set the expressions equal to each other to find when the total costs are the same.
$16.50h + 289 = 18.75h + 274.60$

STEP 6

Solve the equation for $h$ .
Subtract $16.50h$ from both sides: $289 = 2.25h + 274.60$
Subtract $274.60$ from both sides: $289 - 274.60 = 2.25h$
Calculate the left side: $14.40 = 2.25h$
Divide both sides by $2.25$ to solve for $h$ : $h = \frac{14.40}{2.25}$
Calculate the value of $h$ : $h = 6.4$
The number of hours at which the total cost will be the same for both families is $\boxed{6.4}$ .

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Studdy Solution

STEP 1

1. The Smith family's contractor charges $16.50 per hour plus$ 289 in supplies.
2. The Jackson family's contractor charges $18.75 per hour plus$ 274.60 in supplies.
3. We want to find the number of hours at which the total cost for both families is the same.

STEP 2

1. Define variables for the number of hours.
2. Write expressions for the total cost for each family.
3. Set the expressions equal to each other to find the number of hours.
4. Solve the equation for the number of hours.

STEP 3

Define a variable for the number of hours of work. Let $h$ represent the number of hours.

STEP 4

Write expressions for the total cost for each family.
For the Smith family, the total cost is: $C_{\text{Smith}} = 16.50h + 289$
For the Jackson family, the total cost is: $C_{\text{Jackson}} = 18.75h + 274.60$

STEP 5

Set the expressions equal to each other to find when the total costs are the same.
$16.50h + 289 = 18.75h + 274.60$

STEP 6

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Studdy Solution

STEP 1

STEP 2

1. Define variables for the number of hours.2. Write expressions for the total cost for each family.3. Set the expressions equal to each other to find the number of hours.4. Solve the equation for the number of hours.

STEP 3

Define a variable for the number of hours of work. Let h h h represent the number of hours.

STEP 4

Write expressions for the total cost for each family.For the Smith family, the total cost is: CSmith=16.50h+289 C_{\text{Smith}} = 16.50h + 289 CSmith​=16.50h+289For the Jackson family, the total cost is: CJackson=18.75h+274.60 C_{\text{Jackson}} = 18.75h + 274.60 CJackson​=18.75h+274.60

STEP 5

Set the expressions equal to each other to find when the total costs are the same.16.50h+289=18.75h+274.60 16.50h + 289 = 18.75h + 274.60 16.50h+289=18.75h+274.60

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Define variables for the number of hours.
2. Write expressions for the total cost for each family.
3. Set the expressions equal to each other to find the number of hours.
4. Solve the equation for the number of hours.

Define a variable for the number of hours of work. Let $h$ represent the number of hours.

Write expressions for the total cost for each family.
For the Smith family, the total cost is: $C_{\text{Smith}} = 16.50h + 289$
For the Jackson family, the total cost is: $C_{\text{Jackson}} = 18.75h + 274.60$

Set the expressions equal to each other to find when the total costs are the same.
$16.50h + 289 = 18.75h + 274.60$