Final answer:
The inequality to determine the number of quarters in Mr. Umeh's collection, given that he has 50 dimes and a minimum of $10.25, is 0.1x + 0.25y ≥ 10.25, where x is the fixed number of dimes. This is because the value of the dimes and quarters combined must be at least $10.25.
Step-by-step explanation:
The student is asked to determine which inequality can be used to find the number of quarters Mr. Umeh has in his collection given that he has a minimum of $10.25 and 50 dimes. Knowing that there are 100 pennies in one dollar, the value of each dime is $0.10 (or 10 pennies) and the value of each quarter is $0.25 (or 25 pennies). Since we are given the number of dimes (50), we need to find the number of quarters (let's call this y) that make up the minimum total value of $10.25.
Since the dimes contribute $0.10 each, the total contribution of the 50 dimes is $5.00 (50 * $0.10). The rest must come from the quarters. Therefore, the inequality that represents this situation should include the total value of dimes and quarters being greater than or equal to $10.25, hence 0.1(50) + 0.25y ≥ 10.25. This simplifies to 0.1x + 0.25y ≥ 10.25, where x is the constant number of dimes. So, the correct inequality to determine the number of quarters in the collection is choice (a) 0.1x + 0.25y ≥ 10.25.