SOLUTION: There is a test worth 204 total points. The test has true/false questions worth 2 points each. Multiple choice worth 5 points each, and essay questions worth 10 points each. If

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Question 1147757: There is a test worth 204 total points. The test has true/false questions worth 2 points each. Multiple choice worth 5 points each, and essay questions worth 10 points each. If there are 16 more multiple choice questions than true/false, and 7 times as many multiple choice questions as there are essay questions, how many of each type of question are there.
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the number of the true/false questions.


Then the number of the multiple choice questions is (x+14), according to the condition,

and the number of essay questions is %28x%2B14%29%2F7.


The total points is  2x + 5*(x+14) + 10%2A%28%28x%2B14%29%2F7%29.  It is 204, from the other side,

so you have this equation


    2x + 5%2A%28x%2B14%29 + 10%2A%28%28x%2B14%29%2F7%29 = 204.


Now your task is to solve it.  For it, simplify it step by step


    7*(2x) + 7*5*(x+14) + 10*(x+14) = 204*7

    14x + 35x + 490 + 10x + 140 = 1428

    14x + 35x + 10x = 1428 - 490 - 140

    59x             = 798

      x             = 798%2F59 = 12.


ANSWER.  12 true/false questions;  12+16 = 28 multiple choice questions;  and  28%2F7 = 4 essay questions.

Solved.