Question

The sum of four consecutive integers is 90. What is the value of the largest integer?

Option 1: 21
Option 2: 22
Option 3: 23
Option 4: 24

Answer 1

The value of the largest integer among the four consecutive integers is 24 (Option 4).

Step-by-step explanation:

Let's denote the four consecutive integers as
`\(n\), \(n+1\), \(n+2\), and \(n+3\).` The sum of these integers is given by the expression
`\(n + (n+1) + (n+2) + (n+3) = 4n + 6\)` . According to the problem, this sum is equal to 90. Therefore, we can set up the equation
`\(4n + 6 = 90\)` and solve for
`\(n\)` . Subtracting 6 from both sides, we get
`\(4n = 84\),` and dividing by 4 gives
`\(n = 21\).` The largest integer is
`\(n + 3\),` which is
`\(21 + 3 = 24\),` confirming Option 4 as the correct answer.

The algebraic approach involves setting up an equation based on the information provided and solving for the variable
`\(n\).` Once
`\(n\)` is determined, finding the largest integer is a straightforward calculation. The solution aligns with the mathematical principle that the sum of consecutive integers is equal to the average of the integers multiplied by the number of integers.

In summary, (Option 4) the correct answer is obtained through algebraic manipulation, solving the equation, and calculating the largest integer based on the determined value of \(n\). The solution process is concise and aligns with fundamental principles of arithmetic and algebra.