Three consecutive integers have a sum of 258. The smallest of the three integers is \(n\). Write down an equation involving \(n\) and solve it to find the t...
Question 1 Report
Three consecutive integers have a sum of 258. The smallest of the three integers is \(n\). Write down an equation involving \(n\) and solve it to find the three integers. Show your working clearly so that each step can be followed.
Answer Details
Consecutive integers increase by 1 each time, so if the smallest is \(n\), the next two are \(n+1\) and \(n+2\). Writing their sum as an equation turns the word problem into algebra that can be solved directly.
The equation is \(n + (n+1) + (n+2) = 258\).
Collecting like terms on the left gives \(3n + 3 = 258\).
Subtracting 3 from both sides gives \(3n = 255\), and dividing by 3 gives \(n = 85\). [1 mark]
Since \(n\) is the smallest integer, the three consecutive integers are 85, 86 and 87. [1 mark]
A quick check confirms this: \(85 + 86 + 87 = 258\), matching the given total exactly. This "let the unknown be the smallest term" approach works for any set of consecutive integers, since every other term can then be written using only \(n\).
Download The App On Google Playstore
Everything you need to excel in your exams
