a science test, which is worth 100 points, consists of 24 questions. each question is worth either 3 points…

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.\nx + y = 24\n3x + 5y = 100\nwhat does the solution of this system indicate about the questions on the test?\nthe test contains 4 three - point questions and 20 five - point questions.\nthe test contains 10 three - point questions and 14 five - point questions.\nthe test contains 14 three - point questions and 10 five - point questions.\nthe test contains 20 three - point questions and 8 five - point questions.

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.\nx + y = 24\n3x + 5y = 100\nwhat does the solution of this system indicate about the questions on the test?\nthe test contains 4 three - point questions and 20 five - point questions.\nthe test contains 10 three - point questions and 14 five - point questions.\nthe test contains 14 three - point questions and 10 five - point questions.\nthe test contains 20 three - point questions and 8 five - point questions.

Answer

Explanation:

Step1: Solve the first - equation for x

$x = 24 - y$

Step2: Substitute x into the second - equation

$3(24 - y)+5y = 100$

Step3: Expand the left - hand side

$72-3y + 5y=100$

Step4: Combine like terms

$72 + 2y=100$

Step5: Isolate y

$2y=100 - 72$ $2y = 28$ $y = 14$

Step6: Find x

Substitute y = 14 into $x = 24 - y$, we get $x=24 - 14=10$

Answer:

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