RGS P2 Prelims 1998 Q2b
A car travels x km for every litre of petrol used.
(i) Write down an expression for the number of litres used to travel 330 km
A second car travels (x + 4) km for every litre of petrol used.
(ii) Write down an expression for the number of litres this car uses to travel 330 km
Given that the first car uses 8 litres of petrol more than the second car for the 330 km journey, write an equation which x must satisfy and show that it reduces to
x² + 4x - 165 = 0
(iii) Solve this equation, and hence, find the number of litres of petrol used by the second car for the journey.
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Answer:
(i) number of litres = 330 / x
(ii) number of litres = 330 / (x + 4)
330 / x - 330 / (x + 4) = 8
Multiply by x(x + 4) throughout
330 (x + 4) - 330 x = 8 x (x + 4)
330x + 1320 - 330x = 8x² + 32 x
8x² + 32 x - 1320 = 0
Divide by 8 throughout
x² + 4x - 165 = 0 (shown)
(iii) x² + 4x - 165 = 0
(x - 11)(x + 15) = 0
x = 11 or x = -15 (reject because x must be positive)
Hence, number of litres used by second car for the journey = 330 / (11 + 4)
= 330 / 15
= 22 litres
