## Thinking Mathematically (6th Edition)

The numbers are $17$ and $41$.
step 1 Let x represent the smaller number in the problem. step 2 "the other number exceeds x by $24$" = $(x+24)$ "Their sum" = $x+ (x+24)$ step 3 ".. equals $58$" is written as " = $58$". The equation is $x+ (x+24) =58$ step 4 Solve, answer the question. $x+ (x+24) =58 \qquad$ ...simplify the LHS $2x+24=58\qquad/-26$ $2x=34\qquad/\div 2$ $x=17$ The smaller number is 17. The other number is $17+24=41.$ step 5 Check the solution in the original wording of the problem. $41$ exceeds $17$ by $24$. (OK) The sum of $17$ and $41$ is $58$. (OK)