Answer:
The largest consecutive integer is 18.
Step-by-step explanation:
Let the five consecutive integers be [tex]x, x+1, x+2, x+3, x+4[/tex]
The least integer is [tex]x[/tex]and the largest is [tex]x+4[/tex].
It is provided that sum of these 5 integers is 46 less than 9 times the least of integers, i.e.
[tex]x+x+1+ x+2+ x+3+ x+4=9x-46[/tex]
Solve for x as follows:
[tex]x+x+1+ x+2+ x+3+ x+4=9x-46\\5x+10=9x-46\\4x=56\\x=14[/tex]
The largest consecutive integer is:
[tex]x+4=14+4\\=18[/tex]
Thus, the largest consecutive integer is 18.
