How many questions would be worth 2 points and 3 points if a test has 38 questions and a perfect score 100?

Question

An algebra test constrains 38 questions. Some of he questions are with 2 points and some are worth 3 points. A perfect score is 100 points. How many questions would be worth 2 points?

Answer 1

number of 2 point questions= x

number of 3 point questions= y

 

x+y= 38               ____________1

2x+3y=100           ____________2

 

 

x+y=38

x=38-y

 

 

substitute x=38-y in eq 2

 

2(38-y)+3y=100

76-2y+3y=100

 

76+y=100

y=24

 

substitute y=24 in eq 1

 

x+y=38

x+24=38

x=14

 

 

number of 2 point questions= x=14
number of 3 point questions= y=24

 

 

 

Answer 2

Hi Gladys, solve this question by using a system of equations. Let x represent the 2-point questions and y represent the 3-point questions.

 

Equation 1, number of questions:

 

x + y = 38

 

Equation 2, total points:

 

2x + 3y = 100

 

Solve:

 

   x  +   y  =  38

 2x  + 3y  = 100

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

 

Solve by eliminating one variable. I suggest eliminating the x variable.

 

Questions?

Answer 3

let x = # of 2-pt questions; then # of 3-pt questions must be 38-x.

 

2x + 3(38-x) = 100 <<<<< this is the "points accumulation equation.  Solve for x, then you'll know everything.