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

From looking at the second equation 3x + 5y = 100 you can see that x is the number of 3 point questions, y is the number of 5 points questions.

Use the first equation y + x = 24 to substitute into the second equation. You both equations combined into one equation in one variable.
y = 24 - x
sub 24- x in for y

3x + 5(24-x) = 100
3x + 120 - 5x = 100
-2x = 100 - 120
-2x = -20
x = -20/-2
x = 10

then plug this into ether equation to solve for y.

y + 10 = 24
y = 14

10 three pts questions
14 five pts questions

Answer 2

You can solve the system of equations.

Multiply the first equation by -3 and add to the second equation.

-3x - 3y = -72
3x + 5y = 100
(add) --------------------------
2y = 28

y = 14

x + y = 24
x + 14 = 24
x = 10

Answer:
There are 10 3-points questions and 14 5-point questions.

Check: 10 + 14 = 24 There are 24 questions
10 * 3 + 14 * 5 = 30 + 70 = 100 The total number of points is 100.
Our answer is correct.