<< Chapter < Page | Chapter >> Page > |
Let’s study some interesting problems that involve linear equations in one variable. In order to solve such problems, we apply the following five-step method:
If the answer doesn’t check, you have either solved the equation incorrectly, or you have developed the wrong equation. Check your method of solution first. If the result does not check, reconsider your equation.
If it has been your experience that word problems are difficult, then follow the five-step method carefully. Most people have difficulty because they neglect step 1.
Always start by INTRODUCING A VARIABLE!
Keep in mind what the variable is representing throughout the problem.
This year an item costs $44 , an increase of $3 over last year’s price. What was last year’s price?
Step 1:Let x=last year's price.Step 2:x+3=44.x+3 represents the $3 increase in price.Step 3:x+3=44x+3−3=44−3x=41Step 4:41+3=44Yes, this is correct.Step 5:Last year's price was $41.
This year an item costs $23 , an increase of $4 over last year’s price. What was last year’s price?
Last year's price was $19
The perimeter (length around) of a square is 60 cm (centimeters). Find the length of a side.
Step 1:Let x = length of a side.Step 2:We can draw a picture.
Step 3:x+x+x+x=604x=60Divide both sides by 4.x=15.Step 4:4(15)=60.Yes, this is correct.Step 5:The length of a side is 15 cm.
The perimeter of a triangle is 54 inches. If each side has the same length, find the length of a side.
The length of a side is 18 inches.
Six percent of a number is 54. What is the number?
Step 1:Let x= the numberStep 2:We must convert 6% to a decimal.
6%=.06.06x=54.06x occurs because we want 6% of x.Step 3:.06x=54.Divide both sides by .06.x=54.06x=900Step 4:.06(900)=54.Yes, this is correct.Step 5:The number is 900.
Eight percent of a number is 36. What is the number?
The number is 450.
An astronomer notices that one star gives off about 3.6 times as much energy as another star. Together the stars give off 55.844 units of energy. How many units of energy does each star emit?
Let x= number of units of energy given off by the less energetic star. Then, 3.6x= number of units of energy given off by the more energetic star.
Step 2:x+3.6x=55.844.Step 3:x+3.6x=55.8444.6x=55.844Divide both sides by 4.6. A calculator would be useful at thispoint.x=55.8444.6x=12.14The wording of the problem implies two numbers are needed=for a complete solution. We need the number of units ofenergy for the other star.3.6x=3.6(12.14)=43.704Step 4:12.14+43.704=55.844.Yes, this is correct. Step 5:One star gives off 12.14 units of energy and the other star gives off 43.704 units of energy.
Notification Switch
Would you like to follow the 'Elementary algebra' conversation and receive update notifications?