Question

a recipe for lemon bars calls for a 14\ × 13\ pan. how many 1\ × 1\ bars can be cut? how many 3\ × 3\ bars can be cut? how much is wasted if you serve only the 3\ × 3\ square bars? how many 1\ × 1\ bars can be cut? 182 bars (type a whole number.) how many 3\ × 3\ bars can be cut? □ bars (type a whole number.)

Explanation:

Step1: Find number of 3" sides along 14"

To find how many 3 - inch segments fit into 14 inches, we do the division \(14\div3\). Since we are looking for the number of whole 3 - inch lengths, we take the floor of the result. \(14\div3 = 4\) with a remainder of 2 (because \(3\times4 = 12\) and \(14-12 = 2\)). So, we can fit 4 segments of 3 inches along the 14 - inch side.

Step2: Find number of 3" sides along 13"

Similarly, for the 13 - inch side, we divide \(13\div3\). \(13\div3=4\) with a remainder of 1 (because \(3\times4 = 12\) and \(13 - 12=1\)). So, we can fit 4 segments of 3 inches along the 13 - inch side.

Step3: Calculate total number of 3"×3" bars

To find the total number of 3"×3" bars, we multiply the number of 3 - inch segments along each side. So, the total number of bars is \(4\times4 = 16\). (We can also think of it as the area of the pan that can be covered by 3"×3" squares. The area of the pan is \(14\times13 = 182\) square inches (which matches the first part). The area of each 3"×3" bar is \(3\times3=9\) square inches. But if we do \(182\div9\approx20.22\), but this is incorrect because we can't have a fraction of a bar when cutting, we have to consider the number of whole bars that fit along each dimension, which is what we did in the first two steps. So, the correct way is to find how many fit along each side and multiply.)

Answer:

16