Math 112
Instructor: Butler
Problem Solving
Section 3.4
George Polya’s 4-Steps to Problem Solving
1. Understand the Problem – What is the Question?
2. Devise a Strategy/Plan – What don’t we know? What do we know?
Draw a picture, Use a Formula, Write an Equation
3. Carry out that Plan – Solve the Equation
4. Look Back at the Question – Did we Answer the Question? Does it make sense?
Label your answer(s). Check your answer(s).
Write each sentence as an equation. Use x to represent “a number.”
1. Four times a number is 20.
2. The sum of a number and -5 yields 32.
3. Fifteen subtracted from a number amounts to -23.
4. Five times the difference of a number and 7 is equal to -8.
5. The quotient of tripe a number and 5 gives 1.
Problem Solving.
1. Three less than 4 times a number is the same as the number increased by 18. What is the number?
2. The product of a number and 3 is twice the sum of that number and 5. Find the number.
3. You scored 15 points higher on your second exam than you did on your first exam because you
studied more. If the combined score of the two tests is 175, what was your score on your first exam?
4. The perimeter of a rectangle is 300 feet. If the length is 30 less than twice the width, find the
dimensions of the rectangle.
5. Two trains leave Carson City at the same time in opposite directions. After 6 hours, the train going
west was 3 times farther from Carson City than the train going east. How far was the train going east
from Carson City if the distance between the trans was 400 miles?