A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that. Nick only has $10 to spend on washing his car. Let m represent the number of minutes after the initial 5 minutes Nick spends washing his car.
The cost for the initial 5 minutes is $4.
The cost for the additional m minutes is $0.75 * m.
The total cost is $4 + $0.75 * m.
Nick can spend at most $10, so we have the inequality: $4 + $0.75 * m ≤ $10.
Subtracting $4 from both sides of the inequality, we get $0.75 * m ≤ $6.
Dividing both sides of the inequality by $0.75, we get m ≤ 8.
Therefore, Nick can spend at most 8 minutes washing his car.
Let's break down the problem step-by-step.
1. Let's first calculate the amount of money needed for the initial 5 minutes of the car wash.
The car wash charges $4 for the initial 5 minutes, so Nick will spend $4 on the initial 5 minutes.
2. Now, let's determine how much money Nick has left after paying for the initial 5 minutes of the car wash.
Nick initially had $10, and he spent $4 on the initial 5 minutes. Therefore, he has $10 - $4 = $6 left.
3. Next, let's calculate the cost for each additional minute after the initial 5 minutes.
The car wash charges $0.75 for each additional minute, so for m minutes, Nick would need to pay $0.75 * m.
4. Now, let's find the maximum number of additional minutes Nick can afford.
Nick has $6 left, and he needs to pay $0.75 per additional minute. Therefore, the maximum number of additional minutes he can afford is given by:
m = $6 / $0.75 = 8 minutes
So, Nick can spend a maximum of 8 additional minutes washing his car.