I am having trouble with my last two word problems on a homework assignment. For some reason I just can not get word problems and get frusterated. I hope someone can help.

Alan was able to rent a moving van for $99 with unlimited mileage or $49 plus .80 per mile. What mileage would the unlimited mileage plan save money?

A electrician charges $50 for the first half-hour of work and $30 for additional time. Stoney Point High School budgeted $200 to repair the refrigeration system. What length of service call with the budget not be exceeded?

Thank you for helping me to understand.

$99 OR ($49 + .80x) are the possible equations to use on the first one.

($50 + $30x)is the second equation. $200=($50 + $30x)
$200=$80x
divide both sides by 80.
2.5=x
The length of service can be 2 1/2 hours. Hope this helps!

I think there is some confusion here.

Let H = the total hours
$200 = $50 + (H-1)*$30
Remember that the first hour is included in the $50.
subtract $50 from both sides
$150 = (H-1)*$30
divide both sides by $30
5 = H -1
add 1 to both sides:
H = ??

My error

I just reread that the first 1/2 hour is included. I am quite sure that the it is $30 for each additional 1/2 hour
the equation is:
Let H = the number of HALF HOURS
$200 = $50 + (H-1))$30
similarly
$150 = (H-1)*$30
5 = H=1
adding 1 to each side:
H= 6
This is the number of HALF hours.
So, the total HOURS would be:
6/2 = ?

Correcting typo

The line 5 = H = 1
shoud read:
5 = H - 1

I'm sorry to hear that you're having trouble with these word problems, but I'm here to help you understand them! Let's break down each problem and go through the steps to solve them.

1. Alan's Moving Van:
To determine when the unlimited mileage plan saves money compared to the $49 plus $0.80 per mile plan, we need to set up an equation and calculate the mileage threshold.

Let's assume the mileage threshold is "x" miles.

For the unlimited mileage plan, the cost is a flat rate of $99, regardless of the mileage.

For the $49 plus $0.80 per mile plan, the cost can be calculated as follows:
Cost = $49 + ($0.80 * mileage)
Cost = $49 + $0.80x

To find the mileage threshold, we need to set up an equation and solve for "x":
$99 = $49 + $0.80x

Now, let's solve for "x":
$0.80x = $99 - $49
$0.80x = $50

Dividing both sides of the equation by $0.80:
x = $50 / $0.80
x = 62.5 miles

Therefore, if the mileage is greater than 62.5 miles, the unlimited mileage plan would save money.

2. Electrician's Service Call:
To find the length of service call within the budgeted amount of $200, we need to set up an equation and calculate the time threshold.

Let's assume the time threshold is "t" minutes.

For the first half-hour of work, the cost is $50.
For additional time, the cost is $30 per hour (or 60 minutes).

So, for the first half-hour, the cost is $50.
For additional time, the cost can be calculated as follows:
Cost = $30 * (t - 30)

To find the time threshold, we need to set up an equation and solve for "t":
$200 = $50 + $30 * (t - 30)

Now, let's solve for "t":
$200 - $50 = $30(t - 30)
$150 = $30(t - 30)

Dividing both sides of the equation by $30:
5 = t - 30

Adding 30 to both sides of the equation:
t = 5 + 30
t = 35 minutes

Therefore, the length of the service call should not exceed 35 minutes to stay within the budgeted amount of $200.

I hope this helps you understand how to approach and solve word problems. If you have any further questions, feel free to ask!