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The local newspaper sells ads at a constant rate per square inch. A 3-inch-by-4-inch ad costs [tex]\$ 25[/tex]. Susan has a budget of [tex]\$ 150[/tex] to run a 9-inch-by-12-inch ad. Can she purchase a 9-inch-by-12-inch ad and stay within her budget?

A. Yes, because the ad will cost [tex]\$ 75[/tex].
B. Yes, because the ad will cost [tex]\$ 108[/tex].
C. No, because the ad will cost [tex]\[tex]$ 200[/tex].
D. No, because the ad will cost [tex]\$[/tex] 225[/tex].



Answer :

GinnyAnswer
To determine whether Susan can purchase a 9-inch-by-12-inch ad and stay within her budget of [tex]$150, we need to calculate the cost of the larger ad based on the given cost per square inch. Let's work through the problem step-by-step: 1. Find the area of the 3-inch-by-4-inch ad: \[ \text{Area} = 3 \times 4 = 12 \ \text{square inches} \] 2. Determine the cost per square inch for the 3-inch-by-4-inch ad: \[ \text{Cost per square inch} = \frac{25\ \text{dollars}}{12\ \text{square inches}} \approx 2.0833\ \text{dollars per square inch} \] 3. Find the area of the 9-inch-by-12-inch ad: \[ \text{Area} = 9 \times 12 = 108\ \text{square inches} \] 4. Calculate the cost of the 9-inch-by-12-inch ad using the cost per square inch: \[ \text{Cost} = 108 \ \text{square inches} \times 2.0833 \ \text{dollars per square inch} \approx 225\ \text{dollars} \] 5. Compare the cost of the larger ad with Susan's budget: \[ \text{Cost} = 225\ \text{dollars} > 150\ \text{dollars} \] Since the cost of the 9-inch-by-12-inch ad ($[/tex]225) exceeds Susan's budget of [tex]$150, she cannot purchase the ad and stay within her budget. Therefore, the correct answer is: D. No, because the ad will cost $[/tex]225.

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