Your math test has 38 questions and is worth 200 points. The test consists of multiple-choice questions worth 4 points each and open-ended questions worth 20 points each. How many of each type of question are there?

We will give multiple-choice questions the variable #x# and open-ended questions the variable #y#.

Since there are 38 questions total we know that:
#x + y = 38#

We also know that the multiple choice are worth #"4 points"# and the open-ended questions are worth #"20 points"#. The total number of available points is #200# points, so here is our second equation:
#4x + 20y = 200#

Now we can rearrange the first equation so that we are able to substitute it into the second equation:
#x + y = 38#
#x = 38 - y#

Now substitute and solve:

#4x + 20y = 200#

#4(38 - y) + 20y = 200#

#152 - 4y + 20y = 200#

#152 + 16y = 200#

#16y = 48#

#y = 3#

There are 3 open-ended questions.

Now substitute in #3# and solve for #x#:

#x = 38 - y#

#x = 38 - (3)#

#x = 35#

There are 35 multiple choice questions.

Let #x# be the number of multiple choice questions and let #y# be the number of open-ended questions.
#x+y = 38#
#4x + 20y = 200#

Multiplying the first equation by #4#:
#4x + 4y = 152#

Subtracting the second equation from the first equation:
#16y = 48#
#y = 48/16#
#y = 3#

Plugging in #3# for #y# in the first equation:
#x + 3 = 38#
#x = 38-3#
#x = 35#