How to solve algebraic equations using guess and check

• An algebraic equation contains one or more letters in it. Each letter in the equation is called a variable.

• A variable can change in value. We guess at different values for each letter until our equation 'works'.

• We check to see if our answer is too big or too small before we guess another value. The value that works is called the solution.

Guess and check is often used to solve problems. This method is sometimes called Trial and Improvement.

Example:

3 hats and 1 scarf cost £17 altogether. How much does one hat and one scarf cost?

This problem can be written as an equation:

3h + 1s = £17

3h + s = 17

If the scarf costs £5 then we can change the equation to:

3h + 5 = 17

If we try different prices for each hat (h) then we will find the answer that 'works':

Guess h = 6

Check 3 × 6 + 5 = 23

Incorrect: too much

Guess h = 5

Check 3 × 5 + 5 = 20

Incorrect: too much

Guess h = 4

Check 3 × 4 + 5 = 17

Correct!

One hat costs £4

When to use guess and check:

Guess and check is an essential method for any mathematician.

We can also use it for everyday issues, like solving money problems or calculating how long the sides of a perimeter fence in a garden should be (if the amount of fencing is limited).