SOLUTION: Your teacher is giving a test that has 12 more three-point questions than five point questions. The test is worth 100 points. How many of each type of question is on the test? WITH

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Your teacher is giving a test that has 12 more three-point questions than five point questions. The test is worth 100 points. How many of each type of question is on the test? WITH      Log On


   

Question 1065304: Your teacher is giving a test that has 12 more three-point questions than five point questions. The test is worth 100 points. How many of each type of question is on the test? WITH WORK PLEASE
Found 4 solutions by josgarithmetic, josmiceli, MathTherapy, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, how many three-point questions
y, how many five-point questions

system%28x=y%2B12%2C3x%2B5y=100%29

Simply substitute for x into the total-points equation.
3%28y%2B12%29%2B5y=100
3y%2B36%2B5y=100
8y=64
highlight_green%28y=8%29,....

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of 5-point questions
+n+%2B+12+ = the number of 3-point questions
-------------------
+n+%2B+n+%2B+12+=+100+
+2n+%2B+12+=+100+
+2n+=+88+
+n+=+44+
and
+n+%2B+12+=+44+%2B+12+
+n+%2B+12+=+56+
-----------------------
There are 44 5-pt questions
There are 56 3-pt questions

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Your teacher is giving a test that has 12 more three-point questions than five point questions. The test is worth 100 points. How many of each type of question is on the test? WITH WORK PLEASE

Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your teacher is giving a test that has 12 more three-point questions than five point questions. The test is worth 100 points.
How many of each type of question is on the test? WITH WORK PLEASE
~~~~~~~~~~~~~~~~~~~~~~~~ 

Let F be the number of five-point questions.
Then the number of three-point questions is (F + 12).

The "total worth" equation is

5F + 3*(F+12) = 100.

Simplify and solve for F:

5T + 3F + 36 = 100,

8F = 100 - 36  --->  8F = 64  --->  F = 64%2F8 = 8.

Answer. 8 five-point questions and (8+12) = 20 three-point questions.