The product of two consecutive numbers is 14 less than 10th times the smaller number. Find each number.
can you guys explain it too? Thanks!
two consecutive numbers can be represented by n, and n + 1
n(n+ 1) = 10n - 14
n^2 + n = 10n 14 rearrange in to a standard quadratic equation
n^2 - 9n + 14 = 0
(n - 7)(n - 2) = 0
n = 2 or 7. Now you have to try out the answers to see which one works
n = 2, n + 1 = 3
2(3) = 6 ; 10(3) - 14 = 30 - 14 = 16 --> x = 2 is not an answer
n = 7, n + 1 = 8
7(8) = 56 ; 10(7) - 14 = 70 - 14 = 56 --> x = 7 is an answer
7 and 8 are the consecutive numbers
Comments
two consecutive numbers can be represented by n, and n + 1
n(n+ 1) = 10n - 14
n^2 + n = 10n 14 rearrange in to a standard quadratic equation
n^2 - 9n + 14 = 0
(n - 7)(n - 2) = 0
n = 2 or 7. Now you have to try out the answers to see which one works
n = 2, n + 1 = 3
2(3) = 6 ; 10(3) - 14 = 30 - 14 = 16 --> x = 2 is not an answer
n = 7, n + 1 = 8
7(8) = 56 ; 10(7) - 14 = 70 - 14 = 56 --> x = 7 is an answer
7 and 8 are the consecutive numbers