Question

The sum of three consecutive page numbers in a book is 174. What are the page numbers?

Answer 1

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The difference between consecutive numbers is always fixed.

Since it is the page number in a book, the numbers will be a positive integer and will have a difference of 1 between the consecutive numbers as the pages are increasing by 1.

Hence, let the numbers represented by;

`x,(x+1),(x+2)`

Thus, the sum of the three page numbers is 174

`\begin{gathered} x+(x+1)+(x+2)=174 \\ \text{Collecting the like terms,} \\ x+x+x+1+2=174 \\ 3x+3=174 \\ 3x=174-3 \\ 3x=171 \\ \text{Dividing both sides by 3 to find x,} \\ x=(171)/(3) \\ x=57 \end{gathered}`

Hence,

`\begin{gathered} \text{The first of the page number is} \\ x=57 \\ \\ \text{The second is } \\ x+1=57+1 \\ =58 \\ \\ \text{The third page is} \\ x+2=57+2 \\ =59 \end{gathered}`

Therefore, the three consecutive page numbers are 57, 58 and 59