Liam completed three math assignments and got 90% of all questions correct.
Here are his results:
Assignment 1 Assignment 2 Assignment 3
25/30 28/30 ? / 40
How many questions did Liam answer correctly in Assignment 3?
(A) 33 (B) 34 (C) 35 (D) 36
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Let's solve this step by step. Liam completed three math assignments and got 90% of all questions correct. We know his results for Assignment 1 were 25 out of 30, and Assignment 2 were 28 out of 30. We need to find how many questions he answered correctly in Assignment 3, which had 40 total questions.
Now let's calculate the total number of questions. Assignment 1 has 30 questions, Assignment 2 has 30 questions, and Assignment 3 has 40 questions. Adding these together: 30 plus 30 plus 40 equals 100 total questions. This total of 100 questions will serve as our denominator when we calculate the overall percentage.
Now let's apply the overall percentage to find the total correct answers. We know Liam got 90% of all questions correct, and we calculated that there were 100 total questions. So we calculate: 90% of 100 equals 0.90 times 100, which equals 90. This means Liam answered exactly 90 questions correctly across all three assignments combined.
Now let's solve for Assignment 3. We set up the equation: Total equals Assignment 1 plus Assignment 2 plus Assignment 3. Substituting our known values: 90 equals 25 plus 28 plus question mark. First, we add the known correct answers: 25 plus 28 equals 53. Then we subtract from the total: Assignment 3 equals 90 minus 53, which equals 37. So Assignment 3 should have 37 correct answers out of 40 questions.
Let's verify our solution and find the final answer. Our calculation shows that Assignment 3 should have 37 correct answers. We can verify this: 25 plus 28 plus 37 equals 90 total correct answers out of 100 questions, which gives us exactly 90 percent. However, looking at the multiple choice options A through D, we have 33, 34, 35, and 36. Since our calculated answer of 37 is not among the options, the closest available choice is D, 36.