Question 1186022
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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(so_far)}}}?
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<pre>
Let x be the total number of questions in the test.


During first 30 minutes,  {{{x/4}}} questions were answered.


Then 33 additional questions were answered.


Now we have  {{{x/4 + 33}}}  questions answered and  x - {{{(x/4 + 33)}}} = {{{(3/4)x-33}}}  questions unanswered.


The ratio equation is


    {{{(x/4+33)/((3/4)x-33)}}} = {{{4/1}}} = 4.


It means that


    {{{x/4 + 33}}} = {{{4*((3/4)x - 33)}}},

or

    {{{x/4+33}}} = 3x - 132.

    33 + 132 = {{{3x - x/4}}}

    165 = {{{(11/4)x}}}

     x  = {{{(165*4)/11}}} = 60.


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


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

Solved.