My test scores are 75,90,77,88 out of 100. What score on the final paper would I need so that the averages of all scores is at least 83?

You need to write an inequality.

You know the formula for average. You know the number of test scores which is 5. You have one unknown score. You know the other 4.

What do you come up with.

It's actually 6 test scores, 5 of which are known. So sum up the 5 known scores, add X for the unknown 6th score, divide that by 6, and set this equal to 83. Then solve for X. What do you get?