Question

1. Two ski rental companies have different pricing systems. Company A charges a flat fee of $10 plus $5 per hour. Company B does not charge a flat fee but charges $7 per hour rented. After how many hours do both companies charge the same amount?
a. Fill in the equation for the cost of renting skis from Company A.

y = ____ + _____ x

b. Fill in the equation for the cost of renting skis from Company B.

y = _____ x

c. Circle the best method for the cost of renting skis from Company B.

Graphing Substitution Elimination

d. Solve the system using the method you chose.

Rewrite your two equations here. -----------

After ______ hours, both companies charge _____.

e. Check your answer.

Answer 1

Answer:

1a. y = $10 + $5x (With $10 as the flat fee, Company A charges $5 an hour, so the equation should be $10, base, plus $5x, the amount charged after you paid the flat fee.)

1b. y = $7x (Every hour $7 translates to $7x as the total. Nothing more, nothing less.)

1c. Substitution (This will allow us to substitute in one of the equations with y, since the question asks for the same amount charged, with the other equation.)

1d. $10 + $5x = $7x

    $7x - $5x = $10

    $2x = $10

    x = $\frac{\ 10}{\ 2}$

    x = 5

Therefore, after 5 hours, both companies charge $35 dollars.

1e. To check whether this is correct, let's sub in the amount of hours for both equations.

For Company A:

y = $10 + $5x

y = $10 + $5(5)

y = $35

For Company B:

y = $7x

y = $7(5)

y = $35

Since both are equal to $35, we can definitively say the answer is 5 hours.

Step-by-step explanation:

Hope this helped!