The length of a rectangle should be 9 meters longer than 4 times the width. If the length must be between 49 and 85 meters long, what are the restrictions for the width,
w?
asking for _____< or<= w <= or <______
L = 4w+9
if L = 85
w = 76/4 = 19
if L = 49
w = 40/4 = 10
10</= w </= 19
(49 - 9) / 4 =
(85 - 9) / 4 =
To find the restrictions for the width of the rectangle, we can use the given information that the length should be 9 meters longer than 4 times the width. Let's break down the problem step by step:
Step 1: Let's assume that the width of the rectangle is represented by the variable w.
Step 2: According to the given information, the length of the rectangle should be 9 meters longer than 4 times the width. So we can express this as an equation: length = 4w + 9.
Step 3: Further, we know that the length of the rectangle must be between 49 and 85 meters. So we can set up the following inequality: 49 ≤ 4w + 9 ≤ 85.
Step 4: Now, we can solve this inequality to find the restrictions for the width, w.
Let's start by subtracting 9 from all sides of the inequality:
40 ≤ 4w ≤ 76.
Next, divide all sides of the inequality by 4:
10 ≤ w ≤ 19.
Therefore, the restrictions for the width, w, are 10 ≤ w ≤ 19.