Practise the method.
Example 1
An artist sells prints for $60 each. Shop A charges 20% of all sales plus a fixed $27. Shop B charges 25% on the first 4 prints sold, then 10% on further prints, plus a fixed $127. What is the smallest whole number of prints sold for B to leave strictly more money than A?
Show worked answer
Answer: 23
- B costs more during its first 4 sales.
- After those, B saves $6 per further sale.
- Compared with charging 10% throughout, its first sales add $36;
- its fixed charge is $100 higher.
- For n>4, solve 6n>136.
- The smallest whole n is 23.
Example 2
Two accounts start with the same unknown amount. Account A earns 12% simple interest per year for 2 years. Account B earns 12% compound interest per year for 2 years, and receives an extra $1500 immediately after its first year's interest. B finishes $2803.2 ahead of A. What amount, in dollars, did each account start with?
Show worked answer
Answer: 78000
- For starting amount P, A ends at P(1+0.24).
- B ends at P(1.12)2+1500(1.12).
- Their difference gives 0.0144P+1680=2803.2;
- hence P=78000.
Example 3
An artist sells prints for $60 each. Shop A charges 20% of all sales plus a fixed $12. Shop B charges 25% on the first 8 prints sold, then 15% on further prints, plus a fixed $45. What is the smallest whole number of prints sold for B to leave strictly more money than A?
Show worked answer
Answer: 28
- B costs more during its first 8 sales.
- After those, B saves $3 per further sale.
- Compared with charging 15% throughout, its first sales add $48;
- its fixed charge is $33 higher.
- For n>8, solve 3n>81.
- The smallest whole n is 28.