Final answer:
To find the greatest number of newspaper and television ads, we maximize the number of television ads while satisfying the constraint ratio of newspaper to television ads of at least 5 to 3 and staying under the total maximum of 62 ads. By doing so, we calculate a maximum of 23 television ads and 38 newspaper ads, totaling 61 ads.
Step-by-step explanation:
To determine the greatest number of newspaper and television ads that could be bought, we start by understanding that the restaurant can buy up to 62 ads per month and that the ratio of newspaper to television ads must be at least 5 to 3. Let's denote the number of newspaper ads as N and the number of television ads as T.
According to the given ratio, for every 3 television ads, there must be at least 5 newspaper ads. So we can write the inequality 5/3 ≤ N/T. Additionally, the total number of ads cannot exceed 62, which can be expressed as the equation N + T ≤ 62.
To find the maximum number of newspaper ads, we can assume that we buy the maximum number of television ads first and then fill the rest with newspaper ads. This means we want to maximize T with respect to the constraints. Starting with the maximum T that would still allow us to buy at least 5 newspaper ads for every 3 television ads, we increase T until we reach a scenario where N + T equals 62. The last pair of values we find that satisfies both the inequality and the total maximum ads allowed gives us the greatest number of newspaper and television ads we could buy.
For example, if we can buy 3 television ads, then we must buy at least 5 newspaper ads. If we apply this ratio to the maximum number, we find that to maximize T while satisfying N + T ≤ 62, and N/T ≥ 5/3, the greatest number of television ads would be 24 since that would require a minimum of 40 newspaper ads (5/3 of 24), which adds up to 64, slightly over the maximum, so we slightly decrease the number of television ads to meet the limit. Therefore, the maximum number of television ads would be 23 and the maximum number of newspaper ads would be 5/3 * 23 = 38.33, or 38 when rounded down to an integer, making a total of 61 ads.