Question

If the sum of three consecutive numbers is 177 , then the sum of the two lowest values in the series is: A. 115 B. 116 C. 117 D. 118 E. 119

Short answer

The sum of the two lowest consecutive numbers is 117.

Step-by-step solution

Identify Consecutive Numbers

Let's denote the three consecutive numbers as \(x, x+1, x+2\).

Set Up the Equation

According to the problem, the sum of these three consecutive numbers is 177. Thus, the equation becomes \(x + (x+1) + (x+2) = 177\).

Simplify the Equation

Combine like terms to get \(3x + 3 = 177\).

Solve for x

Subtract 3 from both sides: \(3x = 174\). Divide both sides by 3 to obtain: \(x = 58\).

Identify the Numbers

Since \(x = 58\), the three consecutive numbers are: \(58, 59, 60\).

Sum the Two Lowest Numbers

The two lowest numbers are \(58\) and \(59\). Their sum is \(58 + 59 = 117\).

Key concepts

Basic Algebra

Understanding basic algebra is crucial for solving many math problems, including those involving consecutive numbers. In algebra, we often use variables like 'x' to represent unknown values. This allows us to set up equations and solve for these unknowns.

For instance, in the given problem, we let the three consecutive numbers be denoted as \(x, x+1, x+2\). This method helps us easily represent the relationship between these numbers.

Remember, consecutive numbers are numbers that follow each other in sequence, like 5, 6, and 7.

So when dealing with consecutive numbers in algebra, setting up the equation correctly is your first step.

Solving Equations

Solving equations is about finding the value of the unknown variable. Let's look at our consecutive numbers problem.

Once we know our numbers can be represented as \(x, x+1, x+2\), we set up the equation based on the information given. According to the problem, their sum is 177. So, we write:
\(x + (x+1) + (x+2) = 177\).

Next, we simplify the equation by combining like terms. Here we get:
\(x + x + x + 1 + 2 = 177\).
Which simplifies to:
\(3x + 3 = 177\).

The last step is isolating \(x\) by performing inverse operations. Subtract 3 from both sides to get:
\(3x = 174\).
Then, divide both sides by 3:
\(x = 58\).

Thus, we have solved the equation and found the value of the unknown variable.

Arithmetic Operations

Arithmetic operations are the basic calculations we perform in math, such as addition, subtraction, multiplication, and division.

In this problem, we used several arithmetic operations:

• First, addition to set up the initial equation: \(x + (x+1) + (x+2)\).
• Then, combination of like terms is a form of simplification which involves both addition and multiplication: \(3x + 3\).
• Next, subtraction is used to isolate the term with the variable \(3x\): \(3x = 174\).
• Finally, division to solve for the variable \(x = 58\).

These steps showcase how fundamental arithmetic operations are integral to solving algebraic equations.

Additionally, we find the sum of two lowest numbers by simple addition:
\(58 + 59 = 117\).
Mastery of these operations is essential for all further math studies.