Question 766392
find the smallest of 3 consecutive positive integers such that when 5 times the 
largest is subtracted from the square of the middle one the result exceeds three times the smallest by 7.

i cant seem to figure out what "exceeds three times the smallest by 7" part. i get the other part in front. i just need help translating what that part means into algebraic form and i then i can solve the equation.


Let the first of the 3 consecutive positive integers be F
Then the second, or middle integer is F + 1, and the largest is F + 2. I hope you're with me so far!!


{{{(F + 1)^2 - 5(F + 2) = 3F + 7}}} --------- Translating "when 5 times the largest is subtracted from the square of the middle one the result exceeds three times the smallest by 7."


Note that "when 5 times the largest is subtracted from the square of the middle one,"5 times the largest" or 5(F + 2) is subtracted from the square of the middle one ({{{(F + 1)^2}}}) by placing 5(F + 2) after the {{{(F + 1)^2}}}. 


Additionally, note that {{{(F + 1)^2 - 5(F + 2)}}} is LARGER than 3 times the first integer (3F) by 7, so {{{highlight_green((F + 1)^2 - 5(F + 2) = 3F + 7)}}}