Connect quantities, form an equation and interpret an exact solution.
Example 1
Taxi A charges $8.00 plus $1.00 per kilometre. Taxi B charges $30.50 plus $0.25 per kilometre. For what distance, in kilometres, do they cost the same?
Show worked answer
Answer: 30
- Let x be the distance in kilometres.
- 8.00+1.00x=30.50+0.25x.
- Subtract the lower rate and the first fee: 0.75x=22.50.
- So x=30km;
- both fares are $38.00.
Example 2
A tank starts with some water. After 61 of that water is used, 10 litres are added. The tank then contains 80 litres. How many litres were there at the start?
Show worked answer
Answer: 84
- Let x be the initial amount in litres.
- x−6x+10=80.
- Subtract 10:x−6x=70.
- Multiply every term by 6:6x−x=420.
- Collect: 5x=420.
- Divide by 5:x=84 litres.
- Check: 84−14+10=80.
Example 3
A show sells 23 tickets: adult tickets cost $13.00 and child tickets cost $7.00. The total takings are $221.00. How many adult tickets were sold?
Show worked answer
Answer: 10
- Let x be the adult tickets;
- then 23−x are child tickets.
- 13x+7(23−x)=221.
- Expand: 13x+161−7x=221.
- Collect: 6x+161=221.
- Subtract 161:6x=60.
- Divide by 6:x=10.
- Check: 10 adults and 13 children give $221.00.