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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