Question

Sam needs a web designer. Designer A is offering her services for an initial $450 in addition to $105 per hour. Designer B is offering her services for an initial $725 in addition to $50 per hour. When will the two designers charge the same amount of money?

The two designers will charge the same amount of money after
hours.

Answer 1

After 5 hours the two would charge the same amount of money.

Explanation:

Designer A: $450 + ($105/hr)x, where x is the number of hours worked;

Designer B: $725 + ($50/hr)x

Equating these two formulas, we get:

$450 + ($105/hr)x = $725 + ($50/hr)x

Subtracting $450 from both sides: ($55/hr)x = $275

Dividing both sides by $55 yields the number of hours worked:

x = $275/$55 = 5

After 5 hours the two would charge the same amount of money.

Answer 2

5 hours

Explanation:

The cost for designer A

450+105h

The cost for designer B

725+50h

We want to know when the cost is the same

Set the expressions equal

450+105h =725+50h

Subtract 50h from each side

450+105h-50h =725+50h-50h

450+55h = 725

Subtract 450 from each side

450+55h-450 = 725 -450

55h = 275

Divide each side by 55

55h/55 =275/55

h =5

At 5 hours the cost is the same