Question

A test has 19 questions worth a total 100 points. There are ten-point questions and four-point questions. How many questions of each kind?

Answer 1

x + y = 19

10x + 4y = 100

This is a systems of equations.

Isolate x from the first equation:
x = 19 - y

Now, plug it into the second:

10(19 - y) + 4y = 100
190 - 10y + 4y = 100
-6y + 190 = 100
-6y = -90
y = 15

Plug y in and solve for x:
10x + 4(15) = 100
10x + 60 = 100
10x = 40
x = 4

There are four 10-point questions and fifteen 4-point questions.

Answer 2

10 points: 4 questions: 4*10=40
4 points: 15 questions: 4*15=60
60+40=100
hope it helps