It cost a manufacturing company $8 to produce one can of paint. If the initial investment in the production line was $50,000, how many cans of paint must be produced before the average cost per can falls to $10?
avg cost = total cost / total cans
So, you want x such that
(50000+8x)/x = 10
To determine the number of cans of paint that must be produced before the average cost per can falls to $10, we can use the formula for average cost:
Average Cost = Total Cost / Number of Units
Given that the initial investment in the production line was $50,000, we need to consider this as part of the total cost. Let's denote the number of cans of paint produced as 'x'.
The total cost can be calculated as follows:
Total Cost = Initial Investment + (Cost per Can × Number of Cans)
Using the given information:
Total Cost = $50,000 + ($8 × x)
Now, we can set up the equation to solve for 'x':
Average Cost = Total Cost / Number of Units
$10 = ($50,000 + ($8 × x)) / x
To solve this equation, multiply both sides by 'x':
$10 × x = $50,000 + ($8 × x)
Next, subtract ($8 × x) from both sides:
$10 × x - $8 × x = $50,000
Simplifying the left side:
$2 × x = $50,000
Finally, divide both sides by $2 to solve for 'x':
x = $50,000 / $2
x = 25,000
Therefore, the manufacturing company must produce 25,000 cans of paint before the average cost per can falls to $10.
To determine the number of cans that must be produced before the average cost falls to $10, we can use the equation:
Total cost = Initial investment + (Cost per can * Number of cans)
We know that the initial investment was $50,000 and the cost per can is $8. We want to find the number of cans when the average cost falls to $10. Let's denote the number of cans as 'x'.
So, the equation becomes:
$50,000 + ($8 * x) = $10 * x
To solve for 'x', we can rearrange the equation:
$8 * x - $10 * x = $50,000
By combining like terms, we have:
-$2 * x = $50,000
Dividing both sides of the equation by -2 gives us:
x = $50,000 / -$2
The negative sign implies that the number of cans must be positive to make sense in this context. So, we can ignore the negative sign:
x = $50,000 / $2
x = 25,000 cans
Therefore, the manufacturing company must produce 25,000 cans of paint before the average cost per can falls to $10.