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Example 10.38 from Elementary Algebra, 10.4 Solve Applications Modeled by Quadratic Equations
Solve Applications Modeled by Quadratic Equations: example 10.38
The product of two consecutive odd integers is 195. Find the integers.
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 consecutive odd integers. Step 3. Name what we are looking for. Let the first odd integer.
the next odd integerStep 4. Translate into an equation. State the problem in one sentence. "The product of two consecutive odd integers is 195." The product of the first odd integer and the second odd integer is 195. Translate into an equation Step 5. Solve the equation. Distribute. Subtract 195 to get the equation in standard form. Identify the a, b, c values. Write the quadratic equation. Then substitute in the values of a, b, c.. Simplify. Simplify the radical. Rewrite to show two solutions. Solve each equation. There are two values of n that are solutions. This will give us two pairs of consecutive odd integers for our solution. First odd integer
next odd integerFirst odd integer
next odd integerStep 6. Check the answer.
Do these pairs work?
Are they consecutive odd integers?
Is their product 195?Step 7. Answer the question. The two consecutive odd integers whose product is 195 are 13, 15, and −13, −15.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
The product of two consecutive odd integers is 99. Find the integers.
How did it go?