Question

problem 10. (1 point) match each word - problem statement with its correct algebraic translation. 1. the sum of two consecutive even integers is at least 92. 2. one number is 6 more than twice another. the sum of the numbers is 92. 3. jesse has a total of 92 points on the first 6 quizzes in her sociology class. how many total points must she earn on the remaining 5 quizzes in order to have more than 140 points for the semester? 4. the length of a rectangle is 6 in. more than the width. the perimeter of the rectangle is more than 92 in. note: you can earn 30% partial credit for 1 - 2 correct answers, and 60% partial credit for 3 correct answers. a. (x+(x + 2)geq92) b. (x+(x + 92)<92) c. (x+(x + 6)>92) d. (x+(x + 1)geq92) e. (2x+2(x + 6)>92) f. (x+(2x + 6)=92) g. (x + 5x>140) h. (92+x>140) i. none of the above

Explanation:

Step1: Analyze consecutive even integers

Let the first even integer be $x$, then the next consecutive even integer is $x + 2$. The sum is at least 92, so the inequality is $x+(x + 2)\geq92$. This matches option A.

Step2: Analyze the number - relation problem

Let one number be $x$ and the other number is $2x+6$. Their sum is 92, so the equation is $x+(2x + 6)=92$. This matches option F.

Step3: Analyze the quiz - points problem

Jesse has 92 points already. Let the number of points she needs to earn on the remaining quizzes be $x$. She wants more than 140 points in total. So the inequality is $92+x>140$. This matches option H.

Step4: Analyze the rectangle - perimeter problem

Let the width of the rectangle be $x$, then the length is $x + 6$. The perimeter $P=2(x+(x + 6))=2x+2(x + 6)$. Since the perimeter is more than 92, the inequality is $2x+2(x + 6)>92$. This matches option E.

Answer:

1. A. $x+(x + 2)\geq92$
2. F. $x+(2x + 6)=92$
3. H. $92+x>140$
4. E. $2x+2(x + 6)>92$