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4

The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.

Given: Marks scored by Rohit in two tests are 65 and 70.

To find Minimum marks in the third test to make an average of at least 65 marks.

Let marks in the third test be x.

According to the question, we need to find minimum x for which the average of all three papers would be at least 65 marks.

That is,

Average marks in three papers ≥ 65 …(i)

Now, we know that average is given as

So, an average of the marks in these three tests is given by

Substituting this value of average in the inequality (i), we get

⇒ (135 + x) ≥ 65 × 3

⇒ (135 + x) ≥ 195

⇒ x ≥ 195 – 135

⇒ x ≥ 60

This inequality means that Rohit should score at least 60 marks in his third test to have an average of at least 65 marks.

So, the minimum marks to get an average of 65 marks is 60.

Thus, the minimum marks required in the third test is 60.

8

A company manufactures cassettes and its cost and revenue functions for a week are and R = 2x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?