Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Writing equations from a description.
Test Yourself 1.


Basic description. 1. The cost (C) in cents of buying bananas (B) at 40c each and apples (A) at 35c each.
Answer.C = 40B + 35A.

2. The sum of two numbers is 27. If one number is 8:

(i) write an equation to summarise this information.

(ii) Solve your equation to find the other number.

Answer.(i) 8 + x = 27.
(ii) x = 19.

3. I think of a number, add 3 and then double the result. My answer is 28.

(i) write an equation to summarise this information.

(ii) Solve your equation to find the number I thought of.

Answer.Number = 11.
Solving word equations. Write each of the following statements as an equation and then find the value of x:
  4. The perimeter of a rectangle is 28 cm. The longer side is 4 cm longer than the shorter side.

(i) What are the dimensions of the rectangle?

(ii) What is the area of the rectangle?

Answer.(i) Dimensions are 5 × 9 cm.
(ii) Area = 45 cm2
  4. The sum of three consecutive numbers is 51. What are the three numbers?
Answer.The numbers are 16, 17 and 18.
  5. Five times a number less seven is three times the number plus five.

Find the number.

Answer.The number is 6.
  6. When George was 10, his father was three times as old as George.

(i) How old is George's father now?

(ii) In how many years will his father be only twice George's age?

Answer.(i) George's father is now 30.
(ii) In 10 years.
  7. A number (x) is increased by 2 then this amount is multiplied by 3. The result is twice the number.
Answer.x = -6.
  8. When a number (x) is added to 12 and the result is multiplied by 7 and then decreased by 6 the final result is 155.
Answer.x = 11.
  9. The sum of three consecutive odd numbers is 33. Find the numbers.
Answer.The numbers are 9, 11 and 13.
  10. When Ish was 9 years old, her mother was 33. Now Ish's mother is twice as old as Ish. How old are the two ladies now?
Answer.Ish is now 24 and her mother is 48.
Advanced descriptions. 11. In a computer game, I know that the number of "rewards" I earn (N) is calculated according to the rule

"double my strength (S) and three times the number of weapons I have (W) then less a correction factor of 23".

Write an equation allowing me to calculate the number of "rewards" (N) I can earn.

Answer.N = 2S + 3W - 23.
  12. A Bobcat is hired by a farmer to dig trenches on some new paddocks. To transfer the Bobcat to and from the farm costs $850. The cost of using the Bobcat on the farm is $250 per hour.

The hiring company bills the farmer $11,850.

How many hours was the Bobcat used by the farmer?

Answer.44 hours.