Question

Select the correct answer. The number of scented candles packaged in a box can vary by at most two from an average of 80 candles per box. If the cost of producing a candle is two dollars, what is the range of the possible production costs, x, for 50 boxes of candles? A. 78 ≤ x ≤ 82 B. 156 ≤ x ≤ 164 C. 3,900 ≤ x ≤ 4,100 D. 7,800 ≤ x ≤ 8,200

Answer 1

By calculating the cost of producing the minimum and maximum number of candles that can be packaged in 50 boxes, we determine the range of possible production costs, x, is $7,800 to $8,200.

Step-by-step explanation:

The student needs to calculate the range of possible production costs for 50 boxes of candles, given that each box contains an average of 80 candles and the number of candles can vary by at most two from this average. Since each candle costs two dollars to produce, we can find the minimum and maximum number of candles in one box by subtracting and adding two to the average, respectively (78 and 82 candles). Multiplying these numbers by the cost per candle gives us the cost per box, and then multiplying by the number of boxes (50) gives us the total production cost range for all boxes.

To calculate the minimum cost, we use the minimum number of candles per box: 78 candles per box × $2 per candle × 50 boxes = $7,800. To calculate the maximum cost, we use the maximum number of candles per box: 82 candles per box × $2 per candle × 50 boxes = $8,200. Therefore, the range for the possible production costs, x, for 50 boxes of candles is $7,800 ≤ x ≤ $8,200, which corresponds to answer choice D.

Answer 2

Step-by-step explanation:

From the problem statement, each box of candles has the following range of candles:

`78 \leq x \leq 82`

We also know that we have 50 boxes of candles, so we multiply the above range by 50 to get the range of candles:

`3900 \leq x \leq 4100`

Finally, each candle costs $2, so we have the final range of cost:

`7800 \leq x \leq 8200`