Question

Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, i. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, i. What is the maximum length possible for her blanket?

1) 30 inches
2) 45 inches
3) 60 inches
4) 90 inches

Answer 1

The maximum length possible for Charlene's baby blanket is 40 inches.

Step-by-step explanation:

To find the maximum length of Charlene's baby blanket, we need to consider the given conditions. The width of the blanket, w, should be at least half its length, i. The perimeter of the blanket should also be no more than 180 inches. Let's set up the inequalities to represent these conditions:

w ≥ i/2

2w + 2i ≤ 180

Next, we can solve the second inequality for i: i ≤ (180 - 2w)/2. Now let's substitute this expression for i in the first inequality: w ≥ (180 - 2w)/4. Solving for w, we get: w ≥ 60 - 0.5w.

Rearranging the equation, we have 1.5w ≤ 60. Finally, dividing both sides by 1.5, we find that w ≤ 40. Therefore, the maximum length possible for the blanket is 40 inches.