Answer
$x=17$
$y=41$
Work Step by Step
Step 1. Let $x$ and $y$ be the two numbers.
$x$ = the first number
$y$ = the second number
Step 2. Represent other unknown quantities in terms of the other.
Hence, the phrase, "One number exceeds another by 24" --> $x+24=y$
The sum of the numbers is 58 --> $x+y=58$
Step 3. Write the equations that model the conditions.
$x+24=y$ -->equation 1
$x+y=58$ -->equation 2
Step 4. Solve the equation and answer the question.
Substitute equation 1 to equation 2:
$x+(x+24)=58$
$x+x+24=58$
$2x+24=58$
Subtract 24 to both sides:
$2x+24-24=58-24$
$2x=34$
Divide both sides by 2:
$x=17$
Substitute to equation 1:
$x+24=y$
$17+24=y$
$y=41$
Step 5. Check the proposed solution in the original wording of the problem.
Use equation 2:
$x+y=58$
$17+41 = 58$
$58=58$ --> TRUE
