Xiao Gao and Xiao Xin do the same summer homework. When Xiao Gao finishes (1/3), Xiao Xin still has 97 questions left; when Xiao Gao finishes the rest (4/5), Xiao Xin still has all the questions left. (5/9) of the homework has not been completed. Q: How many questions did the teacher assign in total?
小高和小新做同样的暑假作业，当小高完成(1/3)时，小新还剩下97道题没做；当小高完成剩下的(4/5)时，小新还剩下全部作业的(5/9)没有完成．问：老师一共布置了多少道题？
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(2/3) * (4/5)</gadget>
<output>8/15 = around 0.533333</output>

<gadget id="calculator">(1/3) + (8/15)</gadget>
<output>13/15 = around 0.866667</output>

<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>

<gadget id="calculator">1 - (5/9)</gadget>
<output>4/9 = around 0.444444</output>

<gadget id="calculator">(13/15) / (4/9)</gadget>
<output>39/20 = around 1.95</output>

<gadget id="calculator">(1/3) / (39/20)</gadget>
<output>20/117 = around 0.17094</output>

<gadget id="calculator">1 - (20/117)</gadget>
<output>97/117 = around 0.82906</output>

<gadget id="calculator">97 / (97/117)</gadget>
<output>117</output>

<result>117</result>