Number and money problems

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.

To decide which is better value, find the cost of the same amount of each.

1. Pack A: 400 g for £1.60; Pack B: 600 g for £2.16
2. Pack A: 160p ÷ 4 = 40p per 100 g
3. Pack B: 216p ÷ 6 = 36p per 100 g
4. 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.

A bill is usually a fixed part plus a part that depends on use.

1. 45 units at 30p, standing charge 50p a day for 30 days
2. units: 45 × 30 = 1350p
3. standing charge: 30 × 50 = 1500p
4. before VAT: 1350 + 1500 = 2850p = £28.50
5. 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%.

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.