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

The test contains 10 three-point questions and 14 five-point questions

Explanation:

Given equations are:

`x+y = 24\\and\\3x+5y=100`

From 2nd equation we can deduce that x represents number of 3-point questions and y represents number of 5-point questions.

Using the substitution method:

From x+y = 24

y= 24-x

Putting this valu of y in 3x+5y=100

`3x+5(24-x) = 100\\3x + 120 - 5x = 100\\-2x+120=100\\-2x = 100-120\\-2x = -20\\(-2x)/(-2) = (-20)/(-2)\\ x = 10\\Putting\ the\ value\ of\ x\ in\ x+y=24\\10+y=24\\y = 24-10\\y = 14`

Hence, the correct answer is:

The test contains 10 three-point questions and 14 five-point questions..