Question 191032
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We let <font color=blue>x</font> = problems worth 5 points
Also, <font color=blue>y</font> = problems worth 2 points



*Hint:  There are 29 problems.


It follows, <font color=blue>x + y =29</font>,  (EQN 1)



*Note: 
For every  <font color=blue>x</font> problem worth 5 points = "5x", plus for every <font color=blue>y</font> problem worth 2 points = "2y" equals 100 points:


It follows, <font color=blue>5x + 2y =100pts</font>, (EQN 2)



In EQN 1 we get, <font color=blue>x = 29 - y </font> becomes EQN 3 & subst. to EQN 2:
{{{5(highlight(29-y))+2y=100}}}
{{{145-5y+2y=100}}}
Arrange similar terms: (change sign)
{{{145-100=5y-2y}}}
{{{45=3y}}} ----> {{{cross(45)15/cross(3)=cross(3)y/cross(3)}}}
<font color=blue>y = 15 </font>, number of problems for 2 points.



Also, via EQN 3:
{{{x=29-15}}}
<font color=blue>x = 14</font>, number of problem for  5 points.



Check via EQN 2:
{{{5*14+2*15=100pts}}}
{{{70+30=100pts}}}
{{{100pts=100pts}}}



Thank you,
Jojo</font>