Number and money problems
Plan before you calculate
Problem-solving questions do not tell you the steps.
Before you calculate, ask three questions:
- What does the question want at the end: a number, a choice, or yes or no?
- What do I need to find on the way?
- What must I compare, and is it in the same units?
Write each step with a few words, such as "Plan X cost" or "per 100 g". The working earns method marks even if one number slips.
Compare like with like
To decide which is better value, find the cost of the same amount of each.
- Pack A: 400 g for £1.60; Pack B: 600 g for £2.16
- Pack A: 160p ÷ 4 = 40p per 100 g
- Pack B: 216p ÷ 6 = 36p per 100 g
- 36p is less than 40p, so Pack B is better value
The pack that costs less to buy is not always the better value. Compare the cost of the same mass.
Bills and deals
A bill is usually a fixed part plus a part that depends on use.
- 45 units at 30p, standing charge 50p a day for 30 days
- units: 45 × 30 = 1350p
- standing charge: 30 × 50 = 1500p
- before VAT: 1350 + 1500 = 2850p = £28.50
- with 5% VAT: £28.50 × 1.05 = £29.925, so £29.93
For deals, work out the total you pay for the same number of items at each shop. "3 for the price of 2" means you pay for 2. "25% off" means you pay 75%.
Finish with a decision
Many marks are for the conclusion.
Do not stop at a number: answer the question in words and quote the numbers you compared.
Write "Pack B, because 36p per 100 g is less than 40p", not just "B". A choice with no reason usually scores nothing.
Estimate first when a calculator is not allowed: round each number to 1 significant figure. The estimate is a check on the exact answer.
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