Zippy rent a car C=30x+50

Question

Speedy rent a car C =70x+40
The goal is to find the number of days for which both rental locations will cost the same using substitution
Step 1 set the equations equal to each other (since the total cost should be the same) 39x +50=70+40
Step 2 subtract 30x from both sides 50= 40x+40
Step3 subtract 40 from both sides 10= 40x
Step 4 divide by 40 x =1/4
The customer concluded that the rental would be the same after 1/4 day
Identify the mistake and make corrections

Answer 1

Let's closely examine the calculation step-by-step to identify the mistake:

1. Set the equations equal to each other:
   We have two cost equations:

   • Zippy: \( C = 30x + 50 \)
   • Speedy: \( C = 70x + 40 \)

   So, we set them equal to each other:
   \[ 30x + 50 = 70x + 40 \]

2. Subtract \( 30x \) from both sides:
   \[ 50 = 70x - 30x + 40 \]
   \[ 50 = 40x + 40 \]

   This step is correct.

3. Subtract 40 from both sides:
   \[ 50 - 40 = 40x \]
   \[ 10 = 40x \]

   This step is also correct.

4. Divide by 40:
   \[ x = \frac{10}{40} \]
   \[ x = \frac{1}{4} \]

   This is, in fact, where the mistake lies in the interpretation.

The interpretation that "the rental would be the same after 1/4 day" doesn’t make sense in a practical context. Typically, rentals are charged by the full day, and there's no fractional day in rental costs.

The correct conclusion should state:

• The rental costs will be the same after 1/4 of a day, which is equivalent to 6 hours. However, since rental agreements usually cover full days, a customer would need to rent for a minimum of 1 full day to compare costs in practice.

Final Conclusion:

Both rental costs are equal at \( \frac{1}{4} \) of a day, or 6 hours. However, if discussing practical rental costs, the customer would usually rent for at least 1 full day.