SOLVING WORD PROBLEMS USING ALGEBRA

TIP: When doing these sort of problems, remember:

a) Read the problem carefully, then try to assign letters to any unknowns. All algebra
    does is help you to find the unknowns - if you can identify all these you are well on
    the way to solving the problem.

b) Try to identify what sort of problem you are looking at and create suitable equations:
e.g. "Mary buys 3 cans of coke and 4 bags of crisps which cost £2.00, Tim buys 1 can of         coke and 8 bags of crisps for the same price -
        a) how much is a can of coke and
        b) how much is a bag of crisps?"

- this sort of question should be shouting SIMULTANEOUS EQUATION at you.

c) You may not always be required to create new equations yourself, the problems may
    relate to tried and tested equations e.g. Pythagoras' Theorem.

d) Draw a diagram to help you work out what is going on. Remember to put all the
    information on your diagram.

e) Always double check the units in the question to ensure that your calculations and     answers all use consistent units.

Create equations to help you solve these problems:

1.  Jim has 16 coins in his pocket. Some are 10p coins and some are 5p coins. The total value of the coins is £1.25
     how many of each coin does Jim have?
2.  When an object is dropped from a building which is x metres tall, the distance it travels is directly proportional
      to the square of the time taken during its fall.

     When t = 2 seconds, x = 20 metres.
     Calculate the value of x when the time taken is 5     seconds.
3.  A ladder is 4m long and is resting against a wall at the top and is 1m from the wall at the bottom. How high up
     the wall does the ladder reach?

4.  James cycled from home to his friend's house for a distance of 26 km and later on cycled back the same      distance. James' average speed on the way to his friend's house was x km/h.
     On his return journey James cycled 2 km/h quicker as it would get dark soon and his lights were not working,
     so he managed to get back 10 minutes quicker than it took to reach his friends' house originally.

     a) Write in terms of x, the time in hours taken for:
     i) The outward journey
     ii) The return journey

     b) Show that x2 + 2x - 312 = 0
     c) Calculate James' average speed on the return journey.
5. A cuboid has a volume of 60 cm3. It has a square base of length x cm and a height of h cm.
    Find an equation to represent x.
    Hence find x when h = 6 and find h when x = 3.
6. I subtract 5 from a number and multiply the result by 6. The answer is the same as when I multiply the number
    by 5 and subtract 10 from the result. What is the number?
7. Mrs Young is 7 times older than her daughter, but in 25 years' time she will only be twice as old as her daughter.     How old is Mrs Young?

8.  The width of a rectangular area of a field is 4 metres less than its length. The area enclosed is 60m2. Find
     a) The length of the rectangle and hence find b) the width of the rectangle.

Ok Here's the Answers