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.\n\nx + y = 24\n3x + 5y = 100\n\nwhat does the solution of this system indicate about the questions on the test?\n\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.\n\nx + y = 24\n3x + 5y = 100\n\nwhat does the solution of this system indicate about the questions on the test?\n\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

From $x + y=24$, we get $x = 24 - y$.

Step2: Substitute x into the second - equation

Substitute $x = 24 - y$ into $3x + 5y=100$, we have $3(24 - y)+5y = 100$. Expand the left - hand side: $72-3y + 5y=100$. Combine like terms: $72 + 2y=100$. Subtract 72 from both sides: $2y=100 - 72=28$. Divide both sides by 2: $y = 14$.

Step3: Find the value of 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.