A photocopying machine purchased new for $4500 loses $900 in value a each year.
a. Find the book value of the machine after 18 months.
b. When will the book value be $1200?
Assume that each situation can be decribed as a linear equation
HELP!!! I don't know how to set this up but I know the answer
Value = 4500 - 900t, where t is the number of years
a) 18 months ---> t = 1.5
value = 4500 - 1.5(900) = 3150
b)
solve
1200 = 4500 - 900t
the charge for a one day rental of a car from Hawks car rental agency is $24 plus 15 cents for each mile driven.
a) If sarah drives 85 miles in one day, how much is the charge?
b) If a one day rental cost Sarah $42, how far did she drive?
Well, don't worry, I'm here to help you, even if it means making you smile along the way! Let's tackle this problem step by step.
a. To find the book value of the machine after 18 months, we need to determine how much of its value it loses each month. Since it loses $900 in value every year, it means it loses $900/12 each month, which is $75.
So, after 18 months, the machine would have lost 18 * $75 = $1350 in value.
To find the book value, we subtract the amount lost from the original price:
Book Value = Purchase Price - Amount Lost
Book Value = $4500 - $1350 = $3150
Therefore, after 18 months, the book value of the machine would be $3150.
b. Now, let's determine when the book value will reach $1200. We'll use the same logic as in part a.
First, let's set up the equation:
Book Value = Purchase Price - Amount Lost * Time
Since we want the book value to be $1200, we can write this equation as:
$1200 = $4500 - $900 * Time
To solve for Time, we need to isolate it on one side of the equation:
$900 * Time = $4500 - $1200
$900 * Time = $3300
Now, divide both sides by $900:
Time = $3300 / $900
Time = 3.67 years
So, the book value will be $1200 after approximately 3.67 years.
Remember, this is just a humorous way to approach your problem. If you need further assistance, feel free to ask!
To set up the problem, we can use the equation for a straight line:
y = mx + b
where:
y is the book value of the machine after a certain time (in dollars)
x is the time elapsed (in years)
m is the rate of depreciation (in dollars per year)
b is the initial value of the machine (in dollars)
Let's solve the problem step-by-step.
a. Find the book value of the machine after 18 months.
First, we need to convert 18 months into years. There are 12 months in a year, so 18 months is equal to 18/12 = 1.5 years.
Now, we can substitute the given values into the equation:
y = mx + b
m = -$900 (since the machine loses $900 in value each year)
b = $4500 (since the machine was purchased new for $4500)
x = 1.5 (since 1.5 years have elapsed)
Plugging in the values, we have:
y = -$900(1.5) + $4500
y = -$1350 + $4500
y = $3150
Therefore, the book value of the machine after 18 months is $3150.
b. When will the book value be $1200?
Using the same equation, we can set up the problem:
y = mx + b
m = -$900 (since the machine loses $900 in value each year)
b = $4500 (since the machine was purchased new for $4500)
y = $1200 (since we want to find when the book value is $1200)
Plugging in the values, we have:
$1200 = -$900x + $4500
Now, we can solve for x:
-$900x = $1200 - $4500
-$900x = -$3300
Dividing both sides by -$900, we get:
x = $3300 / $900
x = 3.67
Therefore, the book value will be $1200 after approximately 3.67 years.
Sure, I can help you set up the equations to solve these problems step by step.
a. To find the book value of the machine after 18 month, we need to find the initial value minus the depreciation for that period of time. Let's define the initial value as V0 and the depreciation per year as D, where V0 = $4500 and D = $900.
Using a linear equation, we can set up the following equation to represent the book value after t years:
V(t) = V0 - D*t
Since we want to find the book value after 18 months, we need to convert 18 months to years, which is 1.5 years. So, for part (a) the equation is:
V(1.5) = $4500 - $900 * 1.5
Now, let's solve the equation:
V(1.5) = $4500 - $900 * 1.5
V(1.5) = $4500 - $1350
V(1.5) = $3150
Therefore, the book value of the machine after 18 months is $3150.
b. To find when the book value will be $1200, we can set up the following equation:
V(t) = $1200
Substituting the values, we can rewrite the equation as:
$4500 - D*t = $1200
Solving for t, we have:
$4500 - $900*t = $1200
-$900*t = $1200 - $4500
-$900*t = -$3300
Dividing both sides of the equation by -900, we get:
t = -$3300 / -$900
t = 3.67
Therefore, the book value will be $1200 after approximately 3.67 years.
I hope this explanation helps! Let me know if you have any further questions.