How to Solve Algebra Problems Step by Step 5

Imagine that your favorite singer is performing the Star Spangled Banner. Whenever anyone ––  Whitney Houston, Beyonce, or Toby Keith––  sings the national anthem you know to anticipate the artist’s personal twist on the final note. You’re luxuriating in the peaks and valleys of the dawn’s early light and the twilight’s last gleaming. Wait, wait, here comes the big finish. 

“…O’er the land of the free, and the home of the BRAAAAAAAAVE?”

Instead of brave, the final note is timid and flat.

This is what happens in problem solving. The first 4 steps of problem solving are executed properly.

1. Identify the problem.
2. Identify what you know.
3. Make a plan.
4. Carryout the plan.

The last step is where the problem solving concert (yes, Algebra is art!) concludes in harmony or crashes in dissonance.

Two Red Flags That Signal Wrong Answers

• The answer is too large or too small.
• The question remains unanswered.

Example:  Algebra Word Problem

Peter is driving from his house to his company. On Monday morning, Peter drives 6 miles north on Wallisville Road. Then, he drives 8 miles east on Uvalde Road to reach his company. On Tuesday morning, Peter avoids Wallisville and Uvalde Roads. What is the difference between the number of miles Peter drives on Monday and Tuesday mornings?

Carry out the Plan

Peter's journey to his company resembles a right triangle. Your plan calls for the Pythagorean Theorem.

a² + b²= c²
6² + 8² = c²
36 + 64 ⁼ c²
100 = c²

Take the square root of both sides:
c = 10

Answer: 10 miles. STOP! Verify the answer.

Does the Answer Make Sense? 

Did you answer the question, “What is the difference between the number of miles Peter drives on Monday and Tuesday mornings?” No. The answer, 10 miles, is the direct distance between Peter’s House and Peter’s Company.

Make a new plan:

1. Find the direct distance.
2. Add 6 miles + 8 miles to find the total distance travelled on Wallisville and Uvalde Roads.
3. Find the difference between the numbers in steps 1 & 2.

 

1. Direct distance: 10 miles
2. Distance travelled on Wallisville and Uvalde Roads 6 miles +8 miles =14 miles
3. Difference between the numbers: 14 miles – 10 miles = 4 miles. STOP. Verify the Answer.

Did you answer the question? Yes. Does the answer make sense? Because you reviewed the arithmetic, you are certain that the answer is correct.