Question 1181290
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You can certainly solve the problem as the other tutor suggested, using three unknowns, leading to having to solve a system of three equations in those three unknowns to solve the problem.<br>
Your time is far better used if you take the time to set up the problem using a single variable, which means you will only need to solve a single equation.<br>
x = # of 10-point problems
3x = # of 2-point problems (thrice the number of 10-point problems)
6x-10 = # of 5-point problems (10 less than twice the number of 2-point problems)<br>
{{{x+3x+6x-10=50}}}
{{{10x-10=50}}}
{{{10x=60}}}
{{{x=6}}}<br>
It should be easy to finish the problem from there....<br>
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Using a single variable might increase the time required for setting up the problem by 10-20%; but it will decrease the amount of time and effort required to solve the problem by 80-90%.<br>