Question

the sum of two numbers is 112. the smaller is 58 less than the greater. find the numbers. created equations here: solution:

Explanation:

Step1: Define variables

Let the greater number be $x$, and the smaller number be $y$.

Step2: Set up equations

From the problem:

1. Sum of numbers: $x + y = 112$
2. Smaller is 58 less than greater: $y = x - 58$

Step3: Substitute $y$ into first equation

Substitute $y = x - 58$ into $x + y = 112$:
$x + (x - 58) = 112$

Step4: Simplify and solve for $x$

Combine like terms:
$2x - 58 = 112$
Add 58 to both sides:
$2x = 112 + 58 = 170$
Divide by 2:
$x = \frac{170}{2} = 85$

Step5: Solve for $y$

Substitute $x=85$ into $y = x - 58$:
$y = 85 - 58 = 27$

Step6: Verify the solution

Check sum: $85 + 27 = 112$, which matches the given sum.

Answer:

The greater number is 85, and the smaller number is 27.