Question

3.1 solve and graph inequalities: problem 9
(1 point)
match each word - problem statement with its correct algebraic translation.

1. jesse has a total of 96 points on the first 4 quizzes in her sociology class. how many total points must she earn on the remaining 3 quizzes in order to have more than 150 points for the semester?
2. the length of a rectangle is 4 in. more than the width. the perimeter of the rectangle is more than 96 in.
3. jaime has 4 days to complete a 150 - page reading assignment. how many pages must he read the first day so that he has no more than 96 pages left to read on the 3 remaining days?
4. one number is 4 more than twice another. the sum of the numbers is 96.

a. 96 + x>150
b. x+(x + 2)≥96
c. x+(x + 1)≥96
d. x+(2x + 4)=96
e. 96+3x>150
f. x+(x + 4)>96
g. 2x+2(x + 4)>96
h. 150 - x≤96
i. none of the above
notes: you can earn 30% partial credit for 1 - 2 correct answers and 60% partial credit for 3 correct answers

Explanation:

Step1: Analyze problem 1

Jesse has 96 points on first 4 quizzes and needs more than 150 points in total after 7 quizzes. Let $x$ be the total points on remaining 3 quizzes. The inequality is $96 + x>150$.

Step2: Analyze problem 2

Let width of rectangle be $x$ inches, length is $x + 4$ inches. Perimeter $P=2(l + w)=2(x+(x + 4))$. Given $P>96$, so $2(x+(x + 4))>96$.

Step3: Analyze problem 3

Let number of pages read first - day be $x$. Total pages is 150. Remaining pages for 3 days should be no more than 96. So $150 - x\leq96$.

Step4: Analyze problem 4

Let one number be $x$ and the other be $2x + 4$. Their sum is $x+(2x + 4)=96$.

Answer:

1. A. $96 + x>150$
2. G. $2(x+(x + 4))>96$
3. H. $150 - x\leq96$
4. D. $x+(2x + 4)=96$