Question 662517
Find three consecutive multiples of seven such that the product of the largest two exceeds the product of the smallest two by one thousand and seventy-eight
:
Let x = the middle multiple of 7
then
(x-7), x, (x+7) are the three consecutive multiples of 7
:
" the product of the largest two exceeds the product of the smallest two by one thousand and seventy-eight
:
x(x+7) - x(x-7) = 1078
(x^2 + 7x) - (x^2-7x) = 1078
combine like terms, after removing the brackets
x^2 - x^2 + 7x + 7x = 1078
14x = 1078
x = 1078/14
x = 77 is the middle multiple
:
70, 77, 84 are the three multiples
:
:
see if that flies
(84*77) - 70*77) = 1078
6468 - 5390 = 1078