Final answer:
The correct number of boys in Mrs. Patrick's homeroom is 20. This is because 20 is the only number from the given options that, when multiplied by 1.5, results in a whole number, implying a total class size divisible by 3.
Step-by-step explanation:
To solve the question about how many boys are in Mrs. Patrick's homeroom, we need to apply our knowledge of fractions and percentages. The question states that two-thirds of the students are boys. We have four options for the number of boys: 10, 15, 20, or 25. To find the correct answer, it's necessary to infer that the total number of students must be divisible by 3, since we are dealing with thirds.
Consistently, the only option where multiplying the number of boys by 1.5 (the inverse of two-thirds) results in a whole number is option 3: 20 boys. If there are 20 boys in the class, representing two-thirds, multiplying 20 by 1.5 gives us 30, which would be the total number of students. The number 20 is the only one from our options that, when applied in this manner, results in a whole number, thus, it must be the correct answer. This tells us that there are three groups of 20 making up the full class of students, and two of those groups, or two-thirds, are boys.