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
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 $\boxed{6.4}$.