A printed page is to have a total area of 100 square inches. The top and bottom margins are to be 1 inch and the side margins to be 1.5 inches. Let l represent the total length of the page and w represent the total width of the page.
a) Write an equation, using and , to express the constraint.
b) Write an equation, using and , to express the print area of the page.
c) Write the equation of the print area in terms of only.
for a) I am getting 2l+2w=100... I don't know if this is correct.. and for b and c I don't know how to do it.. help?....thanks ahead
a) To express the constraint of the total area of the page, we can subtract the areas of the margins from the total page area.
The width of the printed area would be the total width minus the sum of the side margins: w - (1.5 + 1.5) = w - 3.
The length of the printed area would be the total length minus the sum of the top and bottom margins: l - (1 + 1) = l - 2.
The area of the printed page would then be the product of the width and length of the printed area: (w - 3)(l - 2).
Therefore, the equation to express the constraint of the total area of the page is: (w - 3)(l - 2) = 100.
b) To express the print area of the page, we need to multiply the width and length of the printed area: (w - 3)(l - 2).
c) To write the equation of the print area in terms of l only, we can substitute the value of w from the constraint equation.
From the constraint equation, we have: 2l + 2w = 100.
Solving for w, we get: w = (100 - 2l)/2 = 50 - l.
Substituting this value of w into the print area equation from part b, we have: [(50 - l) - 3](l - 2) = (50 - l - 3)(l - 2) = (47 - l)(l - 2).