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Example 3.5 from Elementary Algebra, 3.1 Use a Problem-Solving Strategy
Use a Problem-Solving Strategy: example 3.5
One number is five more than another. The sum of the numbers is 21. Find the numbers.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Step 1. Read the problem. Step 2. Identify what we are looking for. We are looking for two numbers. Step 3. Name. We have two numbers to name and need a name for each. Choose a variable to represent the first number. Let number. What do we know about the second number? One number is five more than another. number Step 4. Translate. Restate the problem as one sentence with all the important information. The sum of the 1st number and the 2nd number is 21. Translate into an equation. Substitute the variable expressions. Step 5. Solve the equation. Combine like terms. Subtract 5 from both sides and simplify. Divide by 2 and simplify. Find the second number, too. Step 6. Check. Do these numbers check in the problem? Is one number 5 more than the other? Is thirteen 5 more than 8? Yes. Is the sum of the two numbers 21? Step 7. Answer the question. The numbers are 8 and 13.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.
How did it go?