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Work in either pence or pounds.

£1 = 100p

→ £12 = 10 × 100p = 1200p

To make a profit, the money received must be more than the cost of the buns:

80p × number_of_buns > 1200p

However, as a profit of at least £5 is wanted, this must be added to the cost price to give the amount revenue must exceed:

1200p + £5 = 1200p + 500p = 1700p

This then gives:

80p × number_of_buns > 1700p

→ number_of_buns > 1700p ÷ 80p

→ number_of_buns > 21¼

As only whole buns are being sold, round up to the next whole number and at least that number must be sold:

number_of_buns ≥ 22

→ at least 22 buns need to be sold at 80p to make a profit of at least £5 when it cost £12 to make the buns.

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Lee spent 12 pounds making buns. He sells each bun for 80p. His target is to make a profit of more than 5 pounds. Set up and solve an inequality to work out the least number of buns he must sell to?

Well, honey, to make a profit of more than 5 pounds, Lee should aim to sell buns for more than 17 pounds (12 pounds cost + 5 pounds profit). Since he sells each bun for 80p, which is 0.80 pounds, the inequality to solve is 0.80x > 17, where x is the number of buns Lee must sell. By dividing both sides by 0.80, you find that Lee must sell at least 22 buns to meet his profit target.


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