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?
<pre>Let number of questions be Q
After completing <font size = 5><b>¼</font></b> of the test, he had <font size = 5><b>¾</font></b>  of Q, or {{{3Q/4}}} left to do
He then completed 33 more questions, for a total of {{{Q/4 + 33}}}, and had {{{3Q/4  -  33}}} left to do
We then get: {{{matrix(1,3, (Q/4 + 33)/(3Q/4  -  33), "=", 4/1)}}}
            {{{matrix(1,3, 4(3Q/4 - 33), "=", Q/4 + 33)}}} ----- Cross-multiplying
            {{{matrix(2,3, 3Q  -  132, "=", Q/4 + 33, 3Q  -  Q/4, "=", 33 + 132)}}}
            12Q - Q = 33(4) + 132(4) ------ Multiplying by LCD, 4
            11Q = 165(4)
            Number of questions, or {{{matrix(1,7, Q, "=", 165(4)/11, "=", 15(4), "=", 60)}}}

            Number of questions answered = {{{highlight_green(matrix(1,7, Q/4 + 33, "=", 60/4 + 33, "=", 15 + 33, "=", 48))}}}</pre>