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.
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.
2 answers:
Answer:
The test contains 10 three-point questions and 14 five-point questions.
Step-by-step explanation:
The value of x is the number of 3-point questions, and the value of y is the number of 5-point questions, as the problem statement tells you. So, the solution (x, y) = (10, 14) indicates ...
"The test contains 10 three-point questions and 14 five-point questions."
_____
You can try the offered answers to see which might apply. The last choice has too many questions. The first and third choices don't add up to 100 points.
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To solve for , we need to isolate it on one side of the equation.
Take the square root of both sides, making sure to use both positive and negative roots.
cannot be simplified, so we'll leave it as-is.
Add to both sides to fully isolate
.
Expand the solution by making two solutions, one where is positive and one where it's negative.