Question

The Pleasant Stone Mall charges customers by the minute to use the parking lot. When Zack visited the mall on Monday, he parked for 68 minutes and spent $34 shopping in the mall. When he went on Thursday, he parked for 143 minutes and spent $31 shopping in the mall. That night, he realized he spent the same total amount on parking and shopping each day.
What is the per-minute cost of parking at the mall?

Answer 1

Let \( p \) be the per-minute cost of parking.

On Monday, Zack parked for 68 minutes. The cost of parking that day is:
\[
68p
\]
He spent $34 shopping, so his total expenditure on Monday is:
\[
68p + 34
\]

On Thursday, Zack parked for 143 minutes. The cost of parking that day is:
\[
143p
\]
He spent $31 shopping, so his total expenditure on Thursday is:
\[
143p + 31
\]

According to the problem, Zack spent the same total amount on parking and shopping each day, which gives us the equation:
\[
68p + 34 = 143p + 31
\]

Now, we will solve this equation for \( p \).

First, we can rearrange the equation:
\[
68p + 34 - 31 = 143p
\]
This simplifies to:
\[
68p + 3 = 143p
\]

Next, we will isolate \( p \) by subtracting \( 68p \) from both sides:
\[
3 = 143p - 68p
\]
This simplifies to:
\[
3 = 75p
\]

Now, we can solve for \( p \) by dividing both sides by 75:
\[
p = \frac{3}{75} = \frac{1}{25}
\]

Thus, the per-minute cost of parking at the mall is:
\[
\boxed{0.04}
\]

This means the cost is $0.04 per minute.