Question

Question 5(Multiple Choice Worth 2 points)

(Writing Two-Step Equations MC)
Write and solve an equation that represents the following math sentence.
Twenty-six equals the sum of 13.5 and the quotient of a number and 2.5.
26 13.5+- m=5
m
2.5
26=13.5+m; m = 31.25
2.5
26 13.5+ 2.5m; m = 5
O26 13.5+2.5m; m = 31.25

Answer 1

The math sentence 'Twenty-six equals the sum of 13.5 and the quotient of a number and 2.5' translates to the equation 26 = 13.5 + m/2.5. By isolating the variable and solving the two-step equation, the value for m is found to be 5.

Step-by-step explanation:

The question requires writing and solving an equation that is represented by the math sentence given. To form the equation, we translate the sentence into mathematical terms. 'Twenty-six equals the sum of 13.5 and the quotient of a number and 2.5' can be written as:

26 = 13.5 + ÷ 2.5

To solve this equation, isolate the variable (m) on one side:

1. Subtract 13.5 from both sides of the equation to isolate the terms with the variable.
2. Multiply both sides of the equation by 2.5 to solve for m.

The correct two-step equation representation and solution is:

26 = 13.5 + ÷ 2.5; m = 5

Answer 2

A. 26 = 13.5 + m/2.5; m = 5 is the correct equation and solution.

To explain, the word "quotient" indicates that we need to divide a number by 2.5. Let the unknown number be represented by the variable "m". Then, the quotient of a number and 2.5 can be written as m/2.5. The math sentence can be written as: 26 = 13.5 + m/2.5

To solve for "m", we can isolate it by subtracting 13.5 from both sides and then multiplying both sides by 2.5:

26 - 13.5 = m/2.5

12.5 = m/2.5

m = 12.5 * 2.5

m = 5

Therefore, the equation that represents the given math sentence is 26 = 13.5 + m/2.5, and the solution is m = 5. Option a is correct.