Question

# Use the five-step strategy for solving word problems to find the number or numbers described. One number exceeds another by 24. The sum of the numbers is 58. What are the numbers?

Solution

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Step 1
1 of 2

$\textbf{\color{#4257b2}Step 1: Let $x$ represent one of the unknown quantities.}$

Let $x$ be one of the unknown numbers.

$\textbf{\color{#4257b2}Step 2: Represent other unknown quantities in terms of $x$.}$

Since one number exceeds the other by 24, we represent it as $x+24$.

$\textbf{\color{#4257b2}Step 3: Write an equation in $x$ that models the conditions. }$

We are given that the sum of the two numbers is 58 so we can write the equation:

$x+(x+24)=58$

$\textbf{\color{#4257b2}Step 4: Solve the equation and answer the question.}$

Combine like terms on the left side:

$2x+24=58$

Subtract 26 from both sides:

$2x+24-24=58-24$

Simplify:

$2x=34$

Divide both sides by 2:

$\dfrac{2x}{2}=\dfrac{34}{2}$

Simplify:

$x=17$

So, the two numbers are $\color{#c34632}17$ and $17+24=\color{#c34632}41$.

$\textbf{\color{#4257b2}Step 5: Check the proposed solution in the original wording of the problem.}$

Since $17+41=58$, then our solution is correct.

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