The total cost of manufacturing hundred videotapes is given by the equation. Find if the total cost is $2,100.

Question

The total cost  of manufacturing  hundred videotapes is given by the equation.  Find  if the total cost is $2,100.

Quizplus · Accepted Answer

The equation given is: 
Total cost = (number of videotapes * cost per videotape) + fixed cost

We don't have the values for cost per videotape or fixed cost, but we can still use the equation to find the answer.

Let's say the number of videotapes is x. Then the equation becomes:

Total cost = (x * cost per videotape) + fixed cost

We're given that the total cost is $2,100. So we can write:

$2,100 = (x * cost per videotape) + fixed cost

We don't have enough information to solve for x or cost per videotape or fixed cost individually, but we can still work with the answer choices to see which ones make sense.

Let's try answer choice B: 2 hundred videotapes or 5 hundred videotapes.

If x = 2 hundred videotapes, then the equation becomes:

$2,100 = (2 * 100 * cost per videotape) + fixed cost

Simplifying:

$2,100 = 200 cost per videotape + fixed cost

If x = 5 hundred videotapes, then the equation becomes:

$2,100 = (5 * 100 * cost per videotape) + fixed cost

Simplifying:

$2,100 = 500 cost per videotape + fixed cost

In both cases, we have two unknowns (cost per videotape and fixed cost) and one equation. But notice that in both cases, the number of videotapes is a multiple of 100. That means the cost per videotape and fixed cost must also be in multiples of 100.

Let's look at the other answer choices:

A) 4 hundred videotapes or 10 hundred videotapes - same as B, both have numbers in multiples of 100 
C) 7 hundred videotapes - not a multiple of 100, so the cost per videotape and fixed cost won't be in multiples of 100 
D) 2 hundred videotapes or 10 hundred videotapes - same as A, both have numbers in multiples of 100 
E) 12 hundred videotapes - not a multiple of 100

So answer choice B is the only one that makes sense in terms of the units given (hundred videotapes) and the fact that the cost per videotape and fixed cost must be in multiples of 100.

The Total Cost of Manufacturing Hundred Videotapes Is