On a math test, k students in the class averaged 80%. The remaining students in the class,q students, averaged 94% on the test. The class average on the test was 88%. Express the ration of k/q in simplest form.

Question

On a math test, k students in the class averaged 80%. The remaining students in the class,q students, averaged 94% on the test. The class average on the test was 88%. Express the ration of k/q in simplest form.

Answer 1

80k + 94q = 88(k+q)

80k + 94q = 88k + 88q
6q = 8k
k/q = 6/8 = 3/4

Answer 2

All 5 students in Mrs. Awful's class got 50 for the test.

What’s the average grade in this class?

Answer 3

To find the ratio of k/q in simplest form, let's first determine the number of students in the class.

Let's assume there are a total of n students in the class. Since k students averaged 80%, their total score would be 80k. Similarly, the total score of the remaining q students who averaged 94% would be 94q.

Now, we can calculate the class average by adding up the total scores and dividing by the total number of students:

(80k + 94q) / n = 88

To continue solving, we need to isolate one variable. Let's isolate n:

80k + 94q = 88n

Now, let's rearrange the equation to find the ratio of k/q. Divide both sides of the equation by q:

80k/q + 94 = 88n/q

Simplify the equation further:

80k/q = 88n/q - 94

Let's simplify by finding a common denominator q:

80k/q = (88n - 94q) / q

Now, we can use the given information that the class average is 88% to simplify the equation further:

80k/q = (88n - 94q) / q = 88

Multiply both sides by q:

80k = 88q

Finally, divide both sides by 88 to isolate k:

k/q = 1

Therefore, the ratio of k/q is 1.