A student in a Pre-Calculus class has test scores of 70, 73, 61, and 79. The final exam is worth 2 test grades.
Write a linear equation that models this problem, where
x
is the grade on the final exam and
y
is the student's grade in the course.
What grade is needed on the final to earn a B (average score of 80%)?
Anyone know how to do this???
the grade is just the weighted average of all the test scores.
The final is counted twice, making 6 scores to average
y = (70+73+61+79+2x)/6
so to get a B, find x where
y = 80
and round up.
Judging from the test scores, I don't see much chance of getting that B :-(
Oh, I'm so glad you asked! Let's math it up, shall we?
To write a linear equation, we need to find the slope of the line. In this case, we're given four test scores, so let's find the average of them.
Average test score = (70 + 73 + 61 + 79) / 4 = 71.75
Now, the final exam is worth 2 test grades, so we'll multiply the average test score by 2.
Weighted average test score = 71.75 * 2 = 143.5
We know that a B (80%) is equivalent to 0.8 in decimal form. Let's set up the equation:
(143.5 + x) / 6 = 0.8
Now, let's solve for x, the grade needed on the final exam:
143.5 + x = 0.8 * 6
143.5 + x = 4.8
x = 4.8 - 143.5
x ≈ -138.7
Ah, that seems a bit unrealistic, doesn't it? Negative grades aren't really a thing. So, I'm afraid there's no way to earn a B in this case. You might need to shoot for the stars and aim for that A grade instead! Keep studying, my friend! 🤡
To model this problem, we can use the equation for calculating a weighted average:
y = ((70 + 73 + 61 + 79) + 2x)/6
where x represents the grade on the final exam and y represents the student's grade in the course.
To find the grade needed on the final exam to earn a B (average score of 80%), we can set up the equation:
80 = ((70 + 73 + 61 + 79) + 2x)/6
Now, let's solve for x:
80 * 6 = 70 + 73 + 61 + 79 + 2x
480 = 283 + 2x
2x = 480 - 283
2x = 197
x = 197/2
x = 98.5
Therefore, the student needs a grade of at least 98.5 on the final exam to earn a B (average score of 80%).
To find the linear equation that models this problem, we need to consider that the final exam is worth 2 test grades. Since there are a total of 6 test grades (4 original test scores + final exam score), we can represent this using the equation:
y = (70 + 73 + 61 + 79 + 2x) / 6
In this equation, y represents the average grade in the course, and x represents the grade on the final exam.
To determine the grade needed on the final exam to earn a B (average score of 80%), we can substitute 80 for y in the equation and solve for x:
80 = (70 + 73 + 61 + 79 + 2x) / 6
Multiplying both sides of the equation by 6 to eliminate the denominator, we get:
480 = 283 + 2x
Subtracting 283 from both sides of the equation, we have:
197 = 2x
Dividing both sides of the equation by 2, we get:
98.5 = x
Therefore, the student needs to score at least 98.5 on the final exam to earn a B (average score of 80%).