Number Problem 13 Solution

This is the solution to algebra number problem 13 as asked by an anonymous user: "A maths test contains 10 questions. Ten points are given for each correct answer and three points deducted for an incorrect answer. If Ralph scored 61, how many did he get correct?"

Ok on this problem you can come up with a solution faster by just quick trial an error.  You know that if it only counts 3 points off for each wrong answer and they got a 61 then they had to have at least a 70 before the points were taken off.  If they got a 70 that means they missed 3 problems (3 * 3 = 9)   70 - 9 = 61   .  So the answer is they got 7 problems right and 3 wrong.

Now to set this up using algebra...

10x - 3(10-x) = 61  You are subtracting the wrong answers worth 3  points a piece from the right ones worth 10 a piece.  You don't know how many of each so you are saying there are x amount of 10 valued answers and  (10 - x) number of 3 valued wrong answers. 

10x - (30 - 3x) = 61

10x -30 + 3x = 61

13x = 91  -->   x = 91/13 = 7    --> so there are 7 right 10 valued problems and (10-7) or 3 wrong 3 point negative value ones.....

You could have also set it up like this 10(10 - x) - 3x = 61 and got the same answer....