Question

The larger of two numbers is 7 less than 8 times the smaller. If the larger number is decreased by twice the smaller, the result is 329. Find the two numbers. Define Variables: Equation 1 Equation 2.

Answer 1

The solution to the algebra problem reveals the smaller number is 56 and the larger number is 441, found by setting up two equations based on the given conditions and solving for the variables.

Step-by-step explanation:

Step-by-Step Solution to the Algebra Problem

Let's denote the smaller number as x and the larger number as y. According to the problem, we have two equations.

Equation 1: The larger number is 7 less than 8 times the smaller number. Therefore, y = 8x - 7.

Equation 2: The larger number decreased by twice the smaller number is 329. Therefore, y - 2x = 329.

Now, use Equation 1 to substitute for y in Equation 2:

Substitute x = 56 into Equation 1 to find y:

Therefore, the smaller number is 56 and the larger number is 441.