Acme Movers charges $245 plus $30 per hour to move household goods across town. Hank's Movers charge $65 per hour. For what lengths of time does it cost less to hire Hank's Movers? math problem
let the number of hours be h
Acme: cost = 30h + 245
Hank: cost = 65h
We want to know when they are equal, that is,
when is
65h = 30h + 245
35 h = 245
h = 7
State your conclusion.
Verify my answer by subbing into either of the cost equations
To determine the lengths of time for which it is more cost-effective to hire Hank's Movers, we need to find the time when the cost of Acme Movers is higher than that of Hank's Movers.
Let's assume the number of hours is represented by "x".
For Acme Movers:
Cost = $245 + $30/hour * x
For Hank's Movers:
Cost = $65/hour * x
We want to find the values of x for which the cost of Acme Movers is higher than the cost of Hank's Movers.
$245 + $30x > $65x
Simplifying the equation:
$245 > $65x -$30x
$245 > $35x
Now, we can solve for x by dividing both sides of the inequality by $35:
$245/$35 > $35x/$35
7 > x
So, for any value of x less than 7, it is more cost-effective to hire Hank's Movers.
To determine the length of time for which it is more cost-effective to hire Hank's Movers, we need to calculate the point at which their price is less than Acme Movers.
For Acme Movers, the cost is $245 plus $30 per hour.
For Hank's Movers, the cost is $65 per hour.
Let's assume the number of hours we want to compare for both movers is represented by "x".
So, for Acme Movers, the cost would be: $245 + ($30 * x).
And for Hank's Movers, the cost would be: $65 * x.
To find the point where Hank's Movers are cheaper, we set the two costs equal to each other:
$245 + ($30 * x) = $65 * x
Now we can solve for x.
$245 + $30x = $65x
Subtracting $30x from both sides:
$245 = $35x
Dividing both sides by $35:
$245 / $35 = x
x = 7
So, it costs less to hire Hank's Movers when the length of time needed is less than 7 hours. For 7 hours or more, Acme Movers would be more cost-effective.