Question

match each word problem statement with its correct algebraic translation.

1. the sum of two consecutive even integers is at least 100.
2. the length of a rectangle is 8 in. more than the width. the perimeter of the rectangle is more than 100 in.
3. one number is 8 more than twice another. the sum of the numbers is 100.
4. jesse has a total of 100 points on the first 8 quizzes in her sociology class. how many total points must she earn on the remaining 7 quizzes in order to have more than 145 points for the semester?

Explanation:

Step1: Define variables for consecutive even integers

Let the first even integer be $x$, then the next consecutive even integer is $x + 2$. The sum is at least 100, so the inequality is $x+(x + 2)\geq100$.

Step2: Define variables for rectangle

Let the width of the rectangle be $w$, then the length $l=w + 8$. The perimeter formula is $P=2(l + w)$. Since $P>100$, we have $2((w + 8)+w)>100$.

Step3: Define two - number variables

Let one number be $x$ and the other be $y$. Given $y = 2x+8$ and $x + y=100$.

Step4: Define variable for remaining quizzes points

Let $x$ be the total points on the remaining 7 quizzes. She already has 100 points and wants more than 145 for the semester, so $100+x>145$.

Answer:

1. $x+(x + 2)\geq100$
2. $2((w + 8)+w)>100$
3. $y = 2x+8,x + y=100$
4. $100+x>145$