Final answer:
Anna can afford the largest ad space with dimensions approximately 3.34 inches by 5.01 inches for her budget of $50, where each square inch costs $3 and the advertisement's length and width are in a 3:2 ratio.
Step-by-step explanation:
To determine the largest advertisement Anna can afford in the school newspaper, we need to find the maximum area she can purchase within her budget. Given that each square inch of advertisement space sells for $3, Anna has a maximum of $50 to spend, and she wants a rectangular space with a length and width in the ratio of 3:2.
Let the width of the rectangle be 2x inches and the length be 3x inches (as per the ratio given). The area A of the rectangle will be A = length × width = 3x × 2x = 6x^2 square inches.
Since the cost for each square inch is $3, the total cost of the ad space is 6x^2 × $3. Anna has $50 to spend, so we can set up the equation:
3 × 6x^2 = $50
Solving for x, we get x^2 = $50 / 18 or approximately x^2 = 2.78. Taking the square root of both sides, we get x ≈ 1.67 inches. Therefore, the width will be 2 × 1.67 ≈ 3.34 inches and the length will be 3 × 1.67 ≈ 5.01 inches.
Thus, the largest ad Anna can afford with her budget has dimensions of approximately 3.34 inches by 5.01 inches.