Question

Select the correct answer from each drop-down menu. 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 Nick spends washing his car. Create the inequality that symbolizes this situation. M + ? A car enthusiast magazine recommends spending at least 15 minutes to properly wash a car. Does Nick have enough money to follow this recommendation?

Answer 1

Answer: For $m\geq15$

$\\\Rightarrow\ y=4+0.75(m-5)\geq4+0.75(15-5)\\\Rightarrow\ y\geq4+0.75(10)\\\Rightarrow\ y\geq4+7.5\\\Rightarrow\ y\geq11.5$

Nick does not has enough money to follow this recommendation.

Step-by-step explanation:

Given: A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that.

Let y be the cost for car wash for m minutes then

$y=4+0.75(m-5)$ such that at m= 5 , y=4 which is the cost for car wash (dollars) for first 5 minutes.

Also, A car enthusiast magazine recommends spending at least 15 minutes to properly wash a car.

For $m\geq15$

$\\\Rightarrow\ y=4+0.75(m-5)\geq4+0.75(15-5)\\\Rightarrow\ y\geq4+0.75(10)\\\Rightarrow\ y\geq4+7.5\\\Rightarrow\ y\geq11.5$

But Nick has $10 which is less than $11.5, so he does not has enough money to follow this recommendation.

Answer 2

Answer:

Nick needs $11.50 to wash his car for at least 15 minutes. But, he has only $10. So, he does not have enough money.

Explanation:

Given information : A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that.

Let the cost for car wash for M minutes be = x

Equation forms; $x=4+0.75(M-5)$ ; .....(1)

when M= 5, x=4 (initial 5 minute cost)

Now, we also know that one should spend at least 15 minutes to properly wash a car. So, inequality for number of minutes become $M\geq 15$

Now plugging $M\geq 15$ in equation (1) we get,

$x\geq 4+0.75(15-5)$

$x\geq 4+0.75(10)$

$x\geq 4+7.5$

$x\geq 11.5$

This shows that Nick needs $11.50 to wash his car for at least 15 minutes. But, he has only $10. So, he does not have enough money.