how to write equations

Question

a test hAS 80 QUESTIONS WORTH 100 POINTS. The test consists of true/false questions worth .75 each and multiple choice questions worth 2.75 points each. How many true/false questions are on the test

Answer 1

This problem will give you a system of equations because there are two types of questions.

 

Let x = number of true/false questions and y = number of multiple choice questions.

 

equation 1 →   a total of 80 questions on test so x + y = 80

 

equation 2 →  true/false questions are worth .75 and multiple choice questions are worth 2.75 so

 

                     .75x + 2.75y = 100

 

 

                           x +       y = 80

 

                      .75x + 2.75y = 100

 

 

There are many ways to solve this system. 

 

You could multiply all of equation 1 by .75 and get   .75x +   .75y = 60

 

Put equation 2 under the new equation                   .75x + 2.75y = 100

 

Subtract the 2 equations and get                                      -2.00y = -40

 

Divide both sides by -2 and get                                                y = 20

 

This means there were 20 multiple choice questions.

 

If the total number of questions is 80 you can subtract 20 from 80 and get 60 true/false questions.

 

CHECK

 

60 true/false questions each worth .75 so 60 times .75 = 45 points

 

20 multiple choice questions each worth 2.75 so 20 times 2.75 = 55 points

 

Then add the 45 points and the 55 points gives the necessary total 100 points.

 

 

                                      

Answer 2

Hi Winzetta, 

Step 1: Since there are 80 q's on the test, we can create the following Let Statements:  

Let x= The number of T/F questions

Let 80-x = The number of multiple choice questions 

Step 2: Since we know that each T/F is worth .75, each multiple choice is worth 2.75, and all questions total add up to a 100 points, we can create the equation:

.75x+2.75(80-x)=100

.75x+220-2.75x=100 Now we solve for x

.75x-2.75x=100-220

-2x=-120

x=(-120)/(-2)

x=60

∴There are 60 T/F questions on the test.

Best, 

Star

Answer 3

x= true/false questions

y= multiple choice questions

x+y=80 (total number of questions is 80)

0.75x+2.75y=100 (total number of points is 100 and each true/false question worth 0.75 and each multiple choice question worth 2.75)

 

solve both equations

multiple equation 1 by 0.75 and subtract it from equation 2

-2y=-40 ---->y=20

substitute in the first equation

x+20=80 ---->x=60

 

There fore the test has 60 true/false questions and 20 multiple choice questions

Answer 4

m represents the number of multiple choice questions

80 - m represents the number of true/false questions

 

0.75(80 - m) + 2.75m = 100

60 - 0.75m + 2.75m = 100         combine

60 + 2m = 100                          subtract 60 from both sides

2m = 40                                    divide both sides by 2

m = 20

 

The test has twenty multiple choice questions and sixty true/false questions.

 

Check

 

60(0.75) + 20(2.75)

45 + 55

100