A roll of wrapping paper measures 25 in. × 405 in. The boxes being wrapped are 16 in. × 14 in. × 6 in. How many complete boxes can be wrapped with one roll of wrapping paper?(1 point)$$
To find out how many complete boxes can be wrapped, we need to find the surface area of one box and compare it to the surface area of the wrapping paper.
The surface area of the box is given by the formula:
Surface area = 2*(length*width + length*height + width*height).
Plugging in the numbers for the box, we get:
Surface area of box = 2*(16*14 + 16*6 + 14*6)
= 2*(224 + 96 + 84)
= 2*(404)
= 808.
Now, we need to determine how many times the surface area of one box goes into the surface area of the wrapping paper.
Surface area of wrapping paper = length*width
= 25*405
= 10125.
To find out how many complete boxes can be wrapped, we divide the surface area of the wrapping paper by the surface area of one box:
Number of complete boxes = surface area of wrapping paper/surface area of one box
= 10125/808
= 12.5.
Since we can't have a decimal number of boxes, we need to round down to the nearest whole number.
Therefore, one roll of wrapping paper can wrap 12 complete boxes. Answer: \boxed{12}.