Question

“An A grade will be given to students having at least 450 total test points. There are two more tests to take before the semester is over. Lesha wants to know what she needs to score in order to get an A. Write and solve an equation to determine what score she needs to average on the next two tests if each question is with 1 point. Explain your reasoning.”

Answer 1

The required average on next two tests are:

$t\geq \frac{450-p}{2}$

Solution:

An A grade will be given to students having at least 450 total test points

Let p represent her present test point total, and t represent the necessary average on the next two tests

There are two more tests to take before the semester is over

Therefore,

$p+2t\geq 450$

A grade is given to students having at least 450 total test points

"at least" means greater than or equal to

So we have used greater than or equal to symbol

Solve the inequality for "t"

$p+2t\geq 450\\\\Subtract\ p\ from\ both\ sides\\\\2t\geq 450-p\\\\Divide\ both\ sides\ by\ 2\\\\t\geq \frac{450-p}{2}$

Thus the required average on next two tests are:

$t\geq \frac{450-p}{2}$