Final answer:
Karen's budget for apples and bananas for the daycare next week is more than $20. Using inequalities, this can be represented as 0.50a + 0.20b > $20, reflecting the combined cost of apples and bananas to exceed $20, with 'a' and 'b' indicating the quantity of each fruit.
Step-by-step explanation:
The student has posed a problem involving inequalities and budgeting for buying fruits for a daycare. Based on the given information, to represent the increased budget for apples and bananas Karen plans for the following week, we would set up an inequality that sums the amount spent on apples and bananas to be greater than $20. If we let 'a' represent the number of apples and 'b' represent the number of bananas, and knowing the prices are respectively 50 cents for each apple and 20 cents for each banana, the inequality reflecting next week's planned expenditure would be 0.50a + 0.20b > $20.
The inequality shows that the combination of apples and bananas that Karen buys should total more than $20 in cost, considering the individual prices of each fruit. This budgetary constraint instructs Karen on how to plan her purchases to meet the daycare's needs for the week.