A bus company sells adult tickets and child tickets for a day trip. A child ticket costs £1.30 less than an adult ticket. A family group of 4 adults and 6 c...
Question 1 Report
A bus company sells adult tickets and child tickets for a day trip. A child ticket costs £1.30 less than an adult ticket. A family group of 4 adults and 6 children pays £37.20 in total. The cost of one adult ticket is \(a\) pounds.
- Write down an equation in \(a\). (2)
- Solve your equation to find the cost of an adult ticket. (2)
- Work out the total cost for 3 adults and 5 children. (2)
Answer Details
Two ticket prices are linked by a fixed difference, so both can be written using a single letter. That is what keeps this to one equation rather than a pair of simultaneous equations.
(a) Equation in \(a\). [2]
An adult ticket costs \(a\) pounds, and a child ticket costs £1.30 less, so it costs \((a - 1.30)\) pounds. The group buys 4 adult and 6 child tickets for £37.20:
One mark for the child ticket expression, one for the complete equation. The bracket is essential: all six child tickets are reduced by £1.30 each, not £1.30 in total.
(b) Cost of an adult ticket. [2]
Expand and collect:
An adult ticket costs £4.50. Check: a child ticket is \(4.50 - 1.30 = 3.20\) pounds, and \(4 \times 4.50 + 6 \times 3.20 = 18.00 + 19.20 = 37.20\) pounds, as stated.
(c) Cost for 3 adults and 5 children. [2]
Using £4.50 and £3.20:
The total is £29.50. One mark for the child price, one for the total. Write money answers to two decimal places, so £29.5 should be given as £29.50.
Examination point: when one quantity is described in terms of another, name only the one you are told to name and build the second from it. Introducing a second letter here would leave you with one equation and two unknowns.
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