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Ms. Maynard brought $q$ math quizzes home to grade over the weekend. She could only grade $31$ of the quizzes on Saturday. So, she had $56$ quizzes left to grade on Sunday. $\newline$ Which diagram models the story? $\newline$ Which equation models the story? $\newline$ Choices: $\newline$ (A) $q - 31 = 56$ $\newline$ (B) $q + 31 = 56$

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Find a value using two-variable equations: word problems

Full solution

Q. Ms. Maynard brought

q

math quizzes home to grade over the weekend. She could only grade

31

of the quizzes on Saturday. So, she had

56

quizzes left to grade on Sunday.

\newline

Which diagram models the story?

\newline

Which equation models the story?

\newline

Choices:

\newline

(A)

q - 31 = 56

\newline

(B)

q + 31 = 56

Understand the problem: First, let's understand the problem. Ms. Maynard had a total number of quizzes, $q$ . She graded $31$ on Saturday and had $56$ left for Sunday. We need to find the equation that represents this situation.
Calculate total quizzes: Add the quizzes graded on Saturday to those left for Sunday to find the total. So, $31$ (Saturday's quizzes) + $56$ (Sunday's quizzes) = $87$ . This should give us the total quizzes $q$ .
Check equation choices: Now, let's check the equation choices given: $\newline$ (A) $q - 31 = 56$ $\newline$ (B) $q + 31 = 56$ $\newline$ We need to see which equation correctly calculates the total number of quizzes, $q$ , when solved.
Solve equation (A): Solve equation (A): $\newline$ $q - 31 = 56$ $\newline$ Add $31$ to both sides to isolate $q$ : $\newline$ $q = 56 + 31$ $\newline$ $q = 87$ $\newline$ This matches our calculation from step $2$ .
Verify equation (B): Now, let's check equation (B) for verification: $\newline$ $q + 31 = 56$ $\newline$ Subtract $31$ from both sides: $\newline$ $q = 56 - 31$ $\newline$ $q = 25$ $\newline$ This does not match our total calculated, so it's incorrect.

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