a math test is worth 100 points and has 38 problems. each problem is worth either 5 points or 2 points. how many problems of each point value are on the test?

To answer this, set up a system of equations. What we know is that

5x + 2y = 100
And...
x+y=38

x represents the unknown number of 5 points questions
y represents the unknown number of 2 point questions

In my opinion the easiest way to solve this is to use substitution (that is when you find out the value of one variable, either x or y, and substitute that value as the variable).

So,

x+y=38

Subtract x from both sides

y=38-x

Now, plug (38-x) in as y in the other equation.

5x + 2(38-x) = 100
5x + 76-2x= 100
3x+76=100
3x=24
x=8

Now that you know that x=8, you can solve for y.

5x+2y=100
5(8)+2y=100
40+2y=100
2y=60

2 2
y=30

X=8
Y=30

There are 8 five point questions on the test and 30 two point questions on the test