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.

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?

GPT-4o mini · Answer

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.