Answer:
9 inches high by 6 inches wide
Step-by-step explanation:
Page area is minimized when the aspect ratio is the same as the ratio of margin widths. Here, that means the ratio of height to width should be ...
1.5 : 1 = 3 : 2 = 6 : 4
The latter dimensions for the print area make it be 24 square inches. When 3" of vertical margin and 2 inches of horizontal margin are added, the page size should be 9 inches high by 6 inches wide.
_____
If the width of the paper is x inches, the height is ...
h = 24/(x -2) +3
and the overall area is the product of length and width:
paper area = x(24/(x -2) +3)
Differentiating area with respect to x, we can find the minimum when the derivative is zero.
d(area)/dx = 24/(x -2) +3 -24x/(x -2)² = 0
-3(x² -4x -12)/(x -2)² = 0 . . . . . combine terms
The numerator factors as ...
(x -6)(x +2) = 0
So, the paper width giving minimum area is 6 inches. The height is ...
h = 24(6 -2) +3 = 9 . . . . inches
The least paper is used when the page dimensions are 6 inches wide by 9 inches high.
Answer:
<em>Johnny had </em><em>5</em><em> items and Bobby had </em><em>13</em><em> items.</em>
Step-by-step explanation:
Let us assume that Johnny has x items and Bobby has y items in their list.
Bobby had 3 more than twice as many items on it than Johnny. So,
----------1
Johnny asked for 8 fewer items than bobby. So,
-----------2
Putting the value of x from equation 2 in equation 1, we get
Putting the value of y in equation 2,
So, Johnny had 5 items and Bobby had 13 items.