SOLUTION: Instead of finding even or odd consecutive integers we could also look for integersthat differ by a number other than 2. Find three numbers that each differ by 3 such that 5 times

Question 1048781: Instead of finding even or odd consecutive integers we could also look for integersthat differ by a number other than 2. Find three numbers that each differ by 3 such that 5 times the largest integer is equal to three times the smallest increased by 5 times the middle
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x be the smallest number.
let x + 3 be the middle number.
let x + 6 be the largest number.

your equation is:

5 * (x + 6) = 3 * x + 5 * (x + 3)

this equation says that 5 times the largest number is equal to 3 times the smallest number plus 5 times the middle number.

simplify the equation to get 5x + 30 = 3x + 5x + 15

combine like terms to get 5x + 30 = 8x + 15

subtract 15 from both sides of the equation and subtract 5x from both sides of the equation to get 30 - 15 = 8x - 5x

combine like terms to get 15 = 3x

solve for x to get x = 5

when x = 5, x + 3 = 8, and x + 6 = 11

the difference between each succeeding number is 3.

5 * 11 = 55

3 * 5 + 5 * 8 = 15 + 40 = 55

solution looks good.

the smallest number is 5.
the middle number is 8.
the largest number is 11.

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