#### Question

# Algebra (Word Problem)?

The test consists of 20 questions with the true/false questions worth two points each and the short answer questions worth six points each. If the test is worth 100 points, how many true/false questions are on the test? I was told that the answer is 5, all I need is to see the work on how to get it. Please help I have a test tomorrow and I'm freaking out over this problem.

#### Answers

Make a system of equations.

x = # of true/false questions

y = # of short answer questions

x + y = 20

2x + 6y = 100

Then, multiply the entire top equation by two...

2x + 2y = 40

After that, use elimination, and subtract the first equation from the second...

2x - 2x = 0

6y - 2y = 4y

100 - 40 = 60

so you end up with...

4y = 60

y = 15

So, there are 15 short answer questions, which means there must be 5 true/false questions because there are 20 total questions on the test. To show that mathematically, just plug in the 15 for y in one of the original equations...

x + 15 = 20

Subtract 15 from both sides, so...

x = 5

@Infiniti: There are 20 total questions, not 20 T/F questions.

Let t = # of true/false ?s

Let s = # of short answer questions

solve by system of equations

100 = 2t + 6s ( 100 pts = 2t (2 pts x # of questions) + 6s ( 6pts x # of questions)

20 = t + s ( 20 is the # of questions made up of t (true false) + s (short answer)

--------------------

100 = 2t + 6s

-2(20 = t + s) (multiply both sides of this equation by -2 so that you can add the equations and

-------------------- eliminate a variable )

100 = 2t + 6s

-40 = -2t - 2s ( add the equations)

---------------------

60 = 4s

60/4 = 4s/4 ( divide both sides by 4 to get a single value for # of short answers)

15 = s ( # of short answers)

20 = t + 15

20 - 15 = t + 15 - 15 (subtract 15 from both sides to isolate t)

5 = t ( # of true false questions)