A rail company charges \(2x + 3\) pounds for a peak-time ticket and \(x + 15\) pounds for an off-peak ticket over the same route, where \(x\) is the distanc...
Question 1 Report
A rail company charges \(2x + 3\) pounds for a peak-time ticket and \(x + 15\) pounds for an off-peak ticket over the same route, where \(x\) is the distance travelled in miles.
- The two fares are equal for a particular distance. Find the value of \(x\) by solving \(2x + 3 = x + 15\). (2)
- Give the value of the peak-time fare in pounds for this distance. (2)
Answer Details
Setting two fare expressions equal finds the distance at which the peak-time and off-peak fares cost the same; substituting that distance back into one of the original expressions then gives the actual fare in pounds.
- \(2x + 3 = x + 15\)
Subtracting \(x\) from both sides: \(x + 3 = 15\)
\(x = 12\). [2 marks] - Peak-time fare \( = 2(12) + 3 = 27\) pounds. [2 marks]
As a check, the off-peak fare at this distance is \(12 + 15 = 27\) pounds too, matching the peak-time fare found above, which confirms both fares really do coincide at \(x = 12\) miles.
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