PROBLEM SOLVING

Real World Mixed Problems

Learn the reliable method for real world mixed problems, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A multi-step problem must be broken into connected calculations in a sensible order.

Picture itPlan, solve, then check
2 · THE METHOD

Follow these steps

  1. Identify the final quantity required.
  2. Write the intermediate quantities needed to reach it.
  3. Calculate one stage at a time, keeping units and checking the final result.
3 · WORKED EXAMPLES

See the method in action

Example 1

Of 28 pupils, 12 play chess, 14 play tennis and 3 do both. How many do neither activity?

  1. Adding the activity totals counts the 3 pupils in both groups twice.
  2. The number doing at least one is 12+14−3=23.
  3. Subtract this from 28 to obtain 5.
Answer: 5
Example 2

A tank with vertical sides and a constant horizontal cross-section holds 720 litres at a depth of 80 cm. Water is removed and the depth falls by 20 cm. How much water remains?

  1. The new depth is 60 cm.
  2. Each centimetre of depth represents 720 ÷ 80 = 9 litres, so 60 × 9 = 540 litres remain.
Answer: 540 litres
4 · ELEVENSPRINT TIP

A useful shortcut

Calculate one stage at a time, keeping units and checking the final result.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.