consider two consecutive positive integers such that the square of the second integer added to 5 times the first is equal to 19.

step 1 of 2 : set up an equation to solve the given word problem.

answer

$5x + (x + 1)^2 = 19$
$5x + x + 1 = 19$
$5x^2 + x + 1 = 19$
$x + (x + 1)^2 = 19$

Question

consider two consecutive positive integers such that the square of the second integer added to 5 times the first is equal to 19.

step 1 of 2 : set up an equation to solve the given word problem.

answer

$5x + (x + 1)^2 = 19$
$5x + x + 1 = 19$
$5x^2 + x + 1 = 19$
$x + (x + 1)^2 = 19$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Consecutive Integer Word Problems" ], "new_concepts": [], "current_concepts": [ "Consecutive Integer Word Problems", "Quadratic Word Problems" ] } ## Define consecutive integers Using the *Consecutive Integer Word Problems* knowledge point $$ \begin{aligned} &\text{Let } x \text{ be the first positive integer.}\ &\text{The second consecutive positive integer is } x + 1. \end{aligned} $$ ## Translate the word problem into algebraic terms Using the *Consecutive Integer Word Problems* knowledge point $$ \begin{aligned} &\text{"the square of the second integer": } (x + 1)^2\ &\text{"5 times the first": } 5x\ &\text{"added to": } 5x + (x + 1)^2\ &\text{"is equal to 19": } 5x + (x + 1)^2 = 19 \end{aligned} $$

(A) $5x + (x + 1)^2 = 19$

(B) $5x + x + 1 = 19$

(C) $5x^2 + x + 1 = 19$

(D) $x + (x + 1)^2 = 19$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Consecutive Integer Word Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Define consecutive integers

Translate the word problem into algebraic terms

Answer: