Question

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.

Answer 1

x= # 3-point questions
y= # 5-point questions


QUANTITY EQUATION:
x + y= 24

VALUE EQUATION:
3x + 5y= 100

If we solved these two equations by elimination or substitution, we find x and y. I'm going to solve by elimination.


STEP 1:
multiply the quantity equation by -3 to eliminate the x variable and solve for y.

-3(x + y)= -3(24)
-3x - 3y= -72


STEP 2:
add the value equation and the step 1 equation together to eliminate the x term and solve for y.

3x + 5y= 100
-3x - 3y= -72
the x term is eliminated

2y= 28
divide both sides by 2

y= 14 5-point questions


STEP 3:
substitute the y value into either original equation

x + y= 24

x + 14= 24
subtract both sides by 14

x= 10 3-point questions



ANSWER: The test contains 10 3-point questions and 14 5-point questions.

Hope this helps! :)