Algebra 6

In real life, we rarely get given an equation to solve - we often have to derive it from a problem which is expressed in plain English rather than mathematically.

For example, consider the following simple problem. A shirt has 8 buttons. How many buttons are there on 10 shirts? The equation here (8 x 10 = ?) is not given but it can easily be derived from the information given. And then easily solved to get the answer 80.

Example (Foundation May 15 Paper 2 Q8(b) (i) )

A shirt has b buttons. Write down in terms of b the number of buttons on 10 shirts.

Solution: this is just the previous simple problem with 8 replaced by b. So the answer must be b x 10, which we simply write as 10b. [Don`t let the use of x, b, t or any other symbol confuse the issue. If in doubt just replace them with a number and see what you get. So if you don`t follow this example, replace b with say 5, solve the problem and then ask yourself what you did to 5 to get the answer. Now do the same to b.]

Example (Foundation Jun 14 Paper 2 Q9(b) )

i A ticket costs t pounds. Write down in terns of t the cost of the ticket in pence.

ii Joan is h cm tall. Gill is 3 cm shorter than Joan. Write down Gills height in terns of h

iii A block weighs w kg. Write down in terms of w the weight of 8 such blocks

Sometimes the problems can be a bit more complicated.

Example (Foundation Nov 15 Paper 2 Q8(b) )

Rebecca thinks of a number. She multiplies it by 4 and subtracts 7 to get 41. What was her number?

Solution: in this problem, we do not have an equation. We have a descri ption which we need to convert to an equation. We can then solve it. The way to solve this type of problem is to start by calling the unknown number x. We can then formulate the equation in terms of x.

What happens to x in the descri ption? It is multiplied by 4 and then 7 is subtracted. So we can write

4x - 7

We are told that this is equal to 41. So we can write

4x - 7 = 41.

This is the equation we are after. We can solve it in the usual way. Add 7 to both sides to get

4x - 7 + 7 = 41 + 7

or

4x = 48.

Now divide both sides by 4 to get

x = 12.

Example 1 (Foundation May 15 Q8(b) (ii) )

A total of k blocks are arranged in rows of 5 blocks. There are no blocks left over. Write down in terms of k the number of rows.

Example 2 (Foundation Nov 14 Paper 2 Q9(d) )

Jean rolls a dice many times. She gets a score of 3 on 7 occasions and a score of 4 on n occasions. Write down the total score of these threes and fours in terms of n.

Example 3 (Foundation Nov 14 Paper 1 Q8 )

Gayle buys 8 Biros for £3. Three of them are black. The others are red. Each red Biro costs 45p. What is the cost of one black Biro?