Chapter 2: Q28. (page 94)

Write an equation and solve each problem.
Find four consecutive integers with the sum of 54.

Short Answer

Expert verified

The required consecutive integers are 12, 13, 14 and 15.

Step by step solution

Step 1. List the given data.

The sum of four consecutive integers is 54.

Step 2. Write the equation for the given problem.

Let $x$ be the first integer. Then, the four consecutive integers are $x$ , $x + 1$ , $x + 2$ and $x + 3$ .

Translating the given problem into equation form,

$x + x + 1 + x + 2 + x + 3 = 54$

This is the required equation for the given problem.

Step 3. Solve the equation.

Solving,

$x + x + 1 + x + 2 + x + 3 = 54$ (Obtained equation)

$4 x + 6 = 54$ (Simplify)

$4 x + 6 - 6 = 54 - 6$ (Subtract 6 from both sides)

$4 x = 48$ (Simplify)

$\frac{4 x}{4} = \frac{48}{4}$ (Divide both sides by 4)

$x = 12$ (Simplify)

So, $x = 12$ is the solution of the obtained equation.

Step 4. Interpret the obtained solution.

According to the assumption, $x$ is the first of the four required consecutive integers which satisfy the given problem.

Thus, the required consecutive integers are 12, 13, 14 and 15.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write an equation and solve each problem.
Find four consecutive integers with the sum of 54.

Short Answer

Step by step solution

Step 1. List the given data.

Step 2. Write the equation for the given problem.

Step 3. Solve the equation.

Step 4. Interpret the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Mechanics Maths

Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write an equation and solve each problem.Find four consecutive integers with the sum of 54.

Short Answer

Step by step solution

Step 1. List the given data.

Step 2. Write the equation for the given problem.

Step 3. Solve the equation.

Step 4. Interpret the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Mechanics Maths

Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write an equation and solve each problem.
Find four consecutive integers with the sum of 54.