1. ## Algebra Word Problem

Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17. Multiply the larger of the two numbers by 100, add 50 times the smaller number to that, round the total to the nearest whole number, and what's the answer?

From what I've noticed, the two numbers are not integers. But what ARE the two numbers?

2. Hello, blacksuzaku!

Suppose you have two numbers.
The difference of the two numbers is 12.
The product of the two numbers is 17.

Multiply the larger of the two numbers by 100, add 50 times the smaller number to that,
round the total to the nearest whole number, and what's the answer?

From what I've noticed, the two numbers are not integers.
But what ARE the two numbers?

We have: .x - y .= .12 .[1]
. . . .and: . xy .= .17 . .[2]

From [2], we have: .y = 17/x

Substitute into [1]: .x - 17/x .= .12

Multiply by x: .x² - 17 .= .12x . . x² - 12x - 17 .= .0

. . . . . . . __ . . . . . . - . - . . .__
. . x .= .√53 + 6 .and .y .= .√53 - 6