Final answer:
Solving the equation considering the prices of apples and pears, the lady can buy a maximum of 27 apples and 27 pears with $30 and receive $0.30 back as change. The provided answer options are incorrect. This means she would receive $0.30 in change. So none of the provided answer options A-D are correct.
Step-by-step explanation:
The student wants to calculate the maximum number of fruits (apples and pears) that can be bought with $30, respecting the stipulation that at least 5 of each fruit must be purchased. To solve this, we use the concept of linear equations and inequalities to stay within the budget. The cost of an apple is 45 cents, and a pear is 65 cents. The lady needs to buy at least 5 of each fruit, which means she must spend at least $2.25 on apples (5 apples × $0.45) and $3.25 on pears (5 pears × $0.65) before considering additional fruits. This initial cost is $5.50, leaving her with $24.50 to spend on additional fruits. As the intention is to maximize the number of fruits, we need to calculate the numbers that would allow her to use up as much of the $24.50 as possible without exceeding the budget.
If we denote the number of additional apples she can buy as A and the number of additional pears as P, we have the equations 45A + 65P ≤ 2450 (in cents) and A = P (since the question suggests the same amount of each fruit). By substituting A for P and solving for P, we get P = 2450 / (45 + 65), P = 2450 / 110, P = 22.27, which we round down to 22 to maintain whole fruits for both apples and pears. She can therefore buy 22 additional apples and 22 additional pears, on top of the initial 5, totaling 27 apples and 27 pears.
Finally, we multiply the number of fruits by their respective prices to find out how much change she gets back. That would be (27 apples × $0.45) + (27 pears × $0.65) which equals $12.15 + $17.55 = $29.70. This means she would receive $0.30 in change. So none of the provided answer options A-D are correct. The maximum number of apples and pears she can buy is 27 each, and she will get $0.30 back in change.