A 110 point test is made up of 50 questions. Some qestions are worth 2points and some are worth 4points.how many of each type is on the test?

Question

this is systems of equations and I get so confused when solving them

Answer 1

First, just read and re-read the problem to understand what is being asked, not how to solve it.  This problem asks you to find out how many 2-point and how many 4-point questions there are on this test.  It helps to put the problem into your own words.

 

Next, assign variables.  If possible, assign variable(s) to the value the problem asks you to find (so you won't forget to solve for it at the end).  In this problem, let:

     x = number of 2-point questions

     y = number of 4-point questions

 

Then, translate:

  "50 questions"     means    x + y = 50     [eq1]

  "110 point test ... some 2 points and some 4 points"      means     2x + 4y = 110       [eq2]

     [note:    (points per question)*(number of questions) = points,  because questions cancel out, leaving points]

 

Now, the math is easy (let's use elimination method):

      2x + 4y = 110          [use eq2]

      2x + 2y = 100          [2*eq1 to make coefficients of x equal]    

  ---------------------       [elimination: subtract equations]

              2y =  10

                y =  5           [divide both sides by 2]

 

Use this value of y in either of the first two equations (which one is easier?)

        x + 5 = 50

             x = 45          [subtract 5 from both sides]

 

Checking (very important):

Is    45 + 5 = 50   ?

          50 = 50   ? yes

Is    2(45) + 4(5) = 110   ?

        90   +  20  = 110   ?

              110 = 110   ? yes

Answer 2

Hi Lindeey,

 

Don't get confused. . . just take it step by step by translating the English into math.

 

Let X = the number of 2 point questions.

 

Let Y = the number of 4 point questions.

The number of questions times 2 points plus the number of questions times 4 points equals 110 points.

 

2X + 4Y = 110

 

And the numbers of both types of questions add up to 50.

 

X + Y = 50

 

So now we have two equations and two variables.  Let's rewrite the second equation--> X = 50 -Y

 

and substitute 50 - Y for X in the first equation-->2(50 - Y) + 4Y = 110

 

Get rid of the paretnheses--> 100 - 2Y + 4Y = 110

 

Combine the Y terms and subtract 100 from both sides--> 2Y = 10

 

Divide both sides by 2--> Y = 5

 

So X must be 45

 

Make sure that those numbers work by plugging them back into the question.

 

Have fun.

 

Dan