WORD PROBLEMS

Problem solving strategy

1. Read the whole the question.
2. What are we asked to solve for?
3. Assign a variable to the unknown quantity, for example, x.
4. Translate the words into algebraic expressions by rewriting the given information in terms of the variable.
5. Set up an equation or system of equations to solve for the variable.
6. Solve the equation algebraically using substitution.
7. Check the solution.

Exercise 1: 

Problem 1:

Two jets are flying towards each other from airports that are 1200 km apart. One jet is flying at 250 km/h and the other jet at 350 km/h. If they took off at the same time, how long will it take for the jets to pass each other?

Problem 2:

Kadesh bought 20 shirts at a total cost of R 980. If the large shirts cost R 50 and the small shirts cost R 40. How many of each size did he buy?

Problem 3:

The diagonal of a rectangle is 25$25$ cm more than its width. The length of the rectangle is 17$17$ cm more than its width. What are the dimensions of the rectangle?

Problem 4:

The sum of 27 and 12 is equal to 73 more than an unknown number. Find the unknown number.

Problem 5:

The two smaller angles in a right-angled triangle are in the ratio of 1:2$1:2$. What are the sizes of the two angles?

Problem 6:

The length of a rectangle is twice the breadth. If the area is 128 cm², determine the length and the breadth.

Problem 7:

If 4 times a number is increased by 6, the result is 15 less than the square of the number. Find the number.

Problem 8:

The length of a rectangle is 2$2$ cm more than the width of the rectangle. The perimeter of the rectangle is 20$20$ cm. Find the length and the width of the rectangle.

Problem 9:

Stephen has 1ℓ$1\ell$ of a mixture containing 69%$69\%$ salt. How much water must Stephen add to make the mixture 50%$50\%$ salt? Write your answer as a fraction of a litre.

Problem 10:

The sum of two consecutive odd numbers is 20 and their difference is 2. Find the two numbers.

Problem 11:

The denominator of a fraction is 1 more than the numerator. The sum of the fraction and its reciprocal is 52$\frac{5}{2}$. Find the fraction.

Problem 12:

Masindi is 21 years older than her daughter, Mulivhu. The sum of their ages is 37. How old is Mulivhu?

Problem 13:

Tshamano is now five times as old as his son Murunwa. Seven years from now, Tshamano will be three times as old as his son. Find their ages now.

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