Jason is considering to purchase a new machine to make plastic silverware.the machine produces 1000 pieces of silverware in two hours. one box contains 50 pieces silverware and sells for $3.00.if the machine cost $9000 and runs for 24 hours a day.How many days will it take the machine to make enough silverware to pay for itself?
1000pc/2hr * 24hr/day * 1box/50pc * $3/box * x days = $9000
Now just solve for x
12.5
To calculate the number of days it will take for the machine to pay for itself, we need to find out how many boxes of silverware the machine can produce in 24 hours and then multiply it by the selling price of each box.
First, let's determine how many boxes of silverware the machine can produce in 24 hours.
We know that the machine produces 1000 pieces of silverware in 2 hours. So, it would produce 1000 / 2 = 500 pieces of silverware per hour.
Since each box contains 50 pieces of silverware, the machine would produce 500 / 50 = 10 boxes of silverware per hour.
Now, let's find out how much money the machine can generate in 24 hours by calculating the number of boxes it can produce and multiplying it by the selling price of each box.
In 24 hours, the machine can produce 10 boxes/hour × 24 hours = 240 boxes of silverware.
Multiplying the number of boxes by the selling price, we get 240 boxes × $3.00/box = $720.00.
Since the machine costs $9000.00, we can divide its cost by the amount it generates per day to determine how many days it will take for the machine to pay for itself.
$9000.00 / $720.00/day = 12.5 days.
Therefore, it will take approximately 12.5 days for the machine to make enough silverware to pay for itself.
To determine how many days it will take for the machine to pay for itself, we need to calculate the number of boxes of silverware it will produce in total and then divide it by the number of boxes required to cover its cost. Here are the steps:
Step 1: Calculate the number of silverware pieces produced per hour:
The machine produces 1000 pieces of silverware in 2 hours.
So, it produces 1000/2 = 500 pieces per hour.
Step 2: Calculate the number of silverware pieces produced in a day:
Since the machine runs for 24 hours a day, it will produce 500 * 24 = 12,000 pieces of silverware in a day.
Step 3: Calculate the number of boxes of silverware produced in a day:
A box contains 50 pieces of silverware.
So, the machine will produce 12,000 / 50 = 240 boxes of silverware in a day.
Step 4: Calculate the revenue generated in a day:
Each box sells for $3.00, so the revenue generated in a day will be 240 * $3.00 = $720.00.
Step 5: Calculate the number of days to pay back the machine's cost:
The machine cost $9000. To determine how many days it will take to generate this amount, divide $9000 by $720.00:
$9000 / $720.00 = 12.5 (approx.)
Therefore, it will take approximately 12.5 days for the machine to make enough silverware to pay for itself.