Find 3 consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 5 times the third.
6,7,8
let the first be x-1
let the second be x
let the third be x+1
direct translation from English to Math
(math is a language)
(x-1)(x+2 - x = 5(x+1) + 1
x^2 - 1- x = 5x + 5 + 1
x^2 - 6x -7 = 0
(x-7)(x+1)
x = 7 or x = -1, but x is to be positive
so the first is 6
the second is 7
the third is 8
To find the three consecutive positive integers, let's assign variables to represent the integers. Let's say the first integer is x, the second integer is (x+1), and the third integer is (x+2).
According to the problem, the product of the first and third integers minus the second integer is 1 more than 5 times the third integer. Mathematically, this can be expressed as:
(x)(x+2) - (x+1) = 5(x+2) + 1
Now we can solve the equation to determine the value of x.