7. A student has received scores of 88, 82, and 84 on three quizzes. If tests count twice as much as quizzes, what is the lowest score the student can get on the next test to achieve an average score of at least 70?
A. 13
B. 48
C. 70
D. 96
The correct answer is B, but I would like an explanation on how to get the right answer and how to set up the equation for a problem like this in the future. Thanks.
since tests count twice, add them twice. The total points must be the same as 5 scores of 70:
88+82+84+2x = 70*5
x = 48
Well, we have to help this student out because it looks like they need a little extra credit...in the form of a low score on that next test!
Let's break it down. The student has taken three quizzes and needs to find out the lowest score they can get on the next test to achieve an average score of at least 70.
Since tests count twice as much as quizzes, it means that each test is worth twice as many points as each quiz. So, we'll double the scores of the quizzes to represent their weight in the average calculation.
The total points the student has earned so far are:
88 (quiz) + 82 (quiz) + 84 (quiz) = 254 (total quiz points)
To achieve an average score of at least 70, the student wants to know the minimum total points they need. So, we can set up the equation:
(254 + 2x) / 4 ≥ 70
Where "x" represents the score on the next test. We divide by 4 at the end because the student has taken 3 quizzes and will be taking 1 test.
From there, we can simplify the equation and solve for "x":
254 + 2x ≥ 280
2x ≥ 26
x ≥ 13
So, the lowest score the student can get on the next test to achieve an average score of at least 70 is 13. Option B is the correct answer!
Now, make sure to remind the student that they don't have to clown around—there's always room for improvement! Good luck to them on that next test!
To find the lowest score the student can get on the next test to achieve an average score of at least 70, we'll need to set up an equation.
Let's start by calculating the total scores the student has obtained so far. The quizzes count as 1, and the tests count as 2, meaning we need to double their scores.
Quiz scores:
88 + 82 + 84 = 254
Test scores:
0 (since we don't know the score yet)
Next, we'll calculate the total number of quizzes and tests the student has taken so far.
Quizzes:
3
Tests:
0 (since we haven't taken the next test yet)
Now, we need to find the lowest score the student can get on the next test.
Let's assume the score on the next test is "x."
To achieve an average score of at least 70, the sum of all the scores should be at least (70 * total number of quizzes and tests).
Therefore, we can set up the equation:
(254 + 2x) / (3 + 1) ≥ 70
To simplify the equation, we multiply both sides by (3 + 1):
254 + 2x ≥ 70 * (3 + 1)
254 + 2x ≥ 280
Subtracting 254 from both sides:
2x ≥ 280 - 254
2x ≥ 26
Dividing both sides by 2:
x ≥ 13
Therefore, the lowest score the student can get on the next test to achieve an average score of at least 70 is 13.
So, the correct answer is B. 13.
To solve this problem, we need to find the minimum score the student can get on the next test to achieve an average score of at least 70.
First, we need to calculate the average score of the quizzes. The student received scores of 88, 82, and 84 on the three quizzes. To find the average, we add up the scores and divide by the number of quizzes:
(88 + 82 + 84) / 3 = 254 / 3 ≈ 84.7
Now, we need to consider that tests count twice as much as quizzes. Let's say the student scores x on the next test.
To calculate the average score, we need to take the sum of the scores from quizzes and the double of the score from the next test, and divide it by the total number of items (quizzes + test):
(88 + 82 + 84 + 2x) / 4
Given that we want this average to be at least 70, we can write the following inequality:
(88 + 82 + 84 + 2x) / 4 ≥ 70
Let's solve this inequality step by step:
Multiply both sides of the inequality by 4 to get rid of the fraction:
88 + 82 + 84 + 2x ≥ 280
Add up the numbers on the left side:
254 + 2x ≥ 280
Subtract 254 from both sides:
2x ≥ 26
Finally, divide both sides of the inequality by 2:
x ≥ 13
So, the minimum score the student can get on the next test to achieve an average score of at least 70 is 13. Therefore, the correct answer is B.