Question

An algebra i test contains 40 questions. some of the questions are worth 4 points each, and some are worth 2 points each. the total test is worth 100 points. let f represent the number of questions worth 4 points and t, the number of questions worth 2 points. solve the system by elimination to find the number of four-point questions on the test.

Answer 1

There are 10 four point questions on the test

# of 4 point questions = f
# of 2 point questions = t

total number of questions is 40:
f + t = 40
total number of points is 100:
4f + 2t = 100

f + t = 40
f = -t + 40
substitute "f" with " -t + 40" in the other equation to solve for t
4f + 2t = 100
4(-t + 40) + 2t = 100
-4t + 160 + 2t = 100
-2t + 160 = 100
-2t = -60
t = 30
There are 30 two point questions on the test
now solve for f
f + t = 40
f + (30) = 40
f = 10
the number of four point questions on the test is 10.

Check your work by inputting both variables into either equation:
f + t = 40
(10) + (30) = 40
40 = 40 ✔

4f + 2t = 100
4(10) + 2(30) = 100
40 + 60 = 100
100 = 100 ✔