Question 629795
Let the four numbers be a, b, c, d


(a+b+c+d)/4=40    (Definition of average)


a+b+c+d = 160   (multiply by 4)


c = b + 12   (Given)


b = 5*a      (Given)


d = a - 8    (Given)


c = (5*a) + 12   (Substitution)


Each number has been expressed in terms of "a", we may now solve for "a" by substituting each expression back into the original equation.


a+ 5*a + (5*a + 12) + (a-8) = 160  (Substitution)


a + 5*a + 5*a + 12 + a -8 = 160    (Expansion of terms)


12*a +4 = 160    (add like terms)


12*a = 156       (subtract 4 from both sides)


a = 13   (divide both sides by 4)


With "a" we may solve for each of the other numbers.


b = 5*a = 5*13 = 65  (Substitution and simplify)


c = 5*a + 12 = 5*13 + 12 = 77  (Substitution and simplify)


d = a - 8 = 13 - 8 = 5    (Substitution and simplify)


13 + 65 + 77 + 5 = 160 (Check)