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.

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Find out how to solve algebraic equations using guess and check.

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

Have a go

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YOU WILL NEED - a whiteboard, a ruler, an eraser and some marker pens.
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STEP 1 - Write out the problem. In this case 3 hats and 1 scarf costs £17. If the scarf is £5, how much is 1 hat?
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STEP 2 - You can draw a bar model to help visualise the problem. Include 3 ‘h’ squares (representing the hats), a 5 (representing the scarf) and a 17 (the overall value).
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STEP 3 - Guess that h = 5; this is wrong because the total will equal 20. It is too high.
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STEP 4 - Guess that h = 1; this is wrong because the total will equal 8. It is too low.
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STEP 5 - Guess that h = 4 The total equals 17. This is correct!

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).

Guess and check quiz

Test your knowledge of the guess and check method with this quick quiz.

Where next?

Discover more about this topic from Bitesize.

Algebra

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