SOLUTION: John sat for a Mathematics test. In the first 30 minutes, he had completed 1/4 of the test. In the next hour, he had completed another 33 questions in the ratio of the number o

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: John sat for a Mathematics test. In the first 30 minutes, he had completed 1/4 of the test. In the next hour, he had completed another 33 questions in the ratio of the number o      Log On


   

Question 1186022: John sat for a Mathematics test. In the first 30 minutes, he
had completed 1/4 of the test. In the next hour, he had
completed another 33 questions in the ratio of the number
of questions that were answered to those that were
unanswered became 4:1.
How many questions did he answer altogether?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.
John sat for a Mathematics test. In the first 30 minutes, he
had completed 1/4 of the test. In the next hour, he had
completed another 33 questions in the ratio of the number
of questions that were answered to those that were
unanswered became 4:1.
How many questions did he answer altogether highlight%28so_far%29?
~~~~~~~~~~~~~~~~~~~ 

Let x be the total number of questions in the test.


During first 30 minutes,  x%2F4 questions were answered.


Then 33 additional questions were answered.


Now we have  x%2F4+%2B+33  questions answered and  x - %28x%2F4+%2B+33%29 = %283%2F4%29x-33  questions unanswered.


The ratio equation is


    %28x%2F4%2B33%29%2F%28%283%2F4%29x-33%29 = 4%2F1 = 4.


It means that


    x%2F4+%2B+33 = 4%2A%28%283%2F4%29x+-+33%29,

or

    x%2F4%2B33 = 3x - 132.

    33 + 132 = 3x+-+x%2F4

    165 = %2811%2F4%29x

     x  = %28165%2A4%29%2F11 = 60.


So, 60 questions were there in the test, in all.


Altogether, he answered 60/4 + 33 = 15 + 33 = 48 questions, so far.    ANSWER

Solved.



Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
John sat for a Mathematics test. In the first 30 minutes, he
had completed 1/4 of the test. In the next hour, he had
completed another 33 questions in the ratio of the number
of questions that were answered to those that were
unanswered became 4:1.
How many questions did he answer altogether?
Let number of questions be Q
After completing ¼ of the test, he had ¾  of Q, or 3Q%2F4 left to do
He then completed 33 more questions, for a total of Q%2F4+%2B+33, and had 3Q%2F4++-++33 left to do
We then get: matrix%281%2C3%2C+%28Q%2F4+%2B+33%29%2F%283Q%2F4++-++33%29%2C+%22=%22%2C+4%2F1%29
            matrix%281%2C3%2C+4%283Q%2F4+-+33%29%2C+%22=%22%2C+Q%2F4+%2B+33%29 ----- Cross-multiplying
            
            12Q - Q = 33(4) + 132(4) ------ Multiplying by LCD, 4
            11Q = 165(4)
            Number of questions, or 

            Number of questions answered =