SOLUTION: the length of a rectangle is two meters less than three times its width what is the max integer value of the length if the perimeter is less than 43 meters?

Algebra ->  Rectangles -> SOLUTION: the length of a rectangle is two meters less than three times its width what is the max integer value of the length if the perimeter is less than 43 meters?      Log On


   

Question 882568: the length of a rectangle is two meters less than three times its width what is the max integer value of the length if the perimeter is less than 43 meters?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
L=-2%2B3w and 2w%2B2L%3C43, What is maximum integer value for L?

Could this be done without graphing?
3w-2=L
3w=L%2B2
w=%28L%2B2%29%2F3
-
2%28L%2B2%29%2F3%2B2L%3C43
2L%2F3%2B2%2F3%2B2L%3C43
%282%2F3%2B6%2F3%29L%3C43-2%2F3
Multiply b.s. by 3.
2L%2B6L%3C3%2A43-2
8L%3C127
highlight_green%28L%3C15.875%29

Asked was integer MAX value for LENGTH, but not for width; width not restricted to integers. Allowing for equality perimeter with 43, we can find the width. We already found earlier, w=%28L%2B2%29%2F3;
w=%2815.875%2B2%29%2F3
highlight%28w=5.9833333333%29, repeating 3's.
-
For L to be the largest integer possible, highlight%28L=15%29, while w=5.98333333333.