Question

A science test, which is worth 100 points, consist of 24 questions. Each question is worth either 3 points or 5 points. If X is the number of 3 point questions and why 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?

Answer 1

x= 10 y=14 : 10 3 point, 14 5 point

Explanation:

Write your equation down vertically,

3x + 5y = 100

x + y = 24

Next find multiply bottom equation by one number from the tops opposite,

3x + 5y = 100

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

3x + 5y = 100

-3x - 3y= -72

Add the two functions to isolate y

2y= 28 y=14

Plug y back into original and solve

3x +5(14) =100 --> 3x + 70 =100 --> 3x = 30 x=10