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?

Explanation:

Step1: Define variables

Let \( x \) be the per - minute parking cost (in dollars per minute) and \( y \) be the amount spent on shopping (in dollars).

For Monday, the total cost is the sum of parking cost and shopping cost. The parking cost for 68 minutes is \( 68x \), so the equation for Monday is \( 68x + y=34 \).

For Thursday, the parking cost for 143 minutes is \( 143x \), and the equation for Thursday is \( 143x + y = 31 \). Wait, no, that can't be right. Wait, the problem says "he spent the same total amount on parking and shopping each day". So actually, the total amount (parking + shopping) is the same on both days. So for Monday: \( 68x + y=T \) (where \( T \) is the total amount), and for Thursday: \( 143x + y=T \). Wait, but the shopping amount on Monday is part of the total, and on Thursday, the shopping amount is also part of the total. Wait, the problem says "he spent $34 shopping in the mall" on Monday and "$31 shopping in the mall" on Thursday? Wait, no, re - reading: "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."

So let \( x \) be the per - minute parking cost. Then the total cost on Monday is \( 68x+34 \), and the total cost on Thursday is \( 143x + 31 \). Since the total amounts are equal, we can set up the equation:

\( 68x+34=143x + 31 \)

Step2: Solve for x

Subtract \( 68x \) from both sides:

\( 34=143x - 68x+31 \)

Simplify the right - hand side: \( 143x-68x = 75x \), so the equation becomes \( 34 = 75x+31 \)

Subtract 31 from both sides:

\( 34 - 31=75x \)

\( 3 = 75x \)

Divide both sides by 75:

\( x=\frac{3}{75}=\frac{1}{25}=0.04 \)

Answer:

The per - minute cost of parking is \(\$0.04\) (or 4 cents per minute).