If the price of oranges was raised by \(\frac{1}{2}\)k per orange. The number of oranges a customer can buy for N2.40 will be less by 16. What is the present price of an orange?
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Correct Answer: Option A
Explanation:
Let x represent the price of an orange and
y represent the number of oranges that can be bought
xy = 240k, y = \(\frac{240}{x}\).....(i)
If the price of an oranges is raised by \(\frac{1}{2}\)k per orange, number that can be bought for N240 is reduced by 16
Hence, y - 16 = \(\frac{240}{x + \frac{1}{2}\)
= \(\frac{480}{2x + 1}\)
= \(\frac{480}{2x + 1}\).....(ii)
subt. for y in eqn (ii) \(\frac{240}{x}\) - 16
= \(\frac{480}{2x + 1}\)
= \(\frac{240 - 16x}{x}\)
= \(\frac{480}{2x + 1}\)
= (240 - 16x)(2x + 1)
= 480x
= 480x + 240 - 32x2 - 16
480x = 224 - 32x2
x2 = 7
x = \(\sqrt{7}\)
= 2.5
= 2\(\frac{1}{2}\)k
Let x represent the price of an orange and
y represent the number of oranges that can be bought
xy = 240k, y = \(\frac{240}{x}\).....(i)
If the price of an oranges is raised by \(\frac{1}{2}\)k per orange, number that can be bought for N240 is reduced by 16
Hence, y - 16 = \(\frac{240}{x + \frac{1}{2}\)
= \(\frac{480}{2x + 1}\)
= \(\frac{480}{2x + 1}\).....(ii)
subt. for y in eqn (ii) \(\frac{240}{x}\) - 16
= \(\frac{480}{2x + 1}\)
= \(\frac{240 - 16x}{x}\)
= \(\frac{480}{2x + 1}\)
= (240 - 16x)(2x + 1)
= 480x
= 480x + 240 - 32x2 - 16
480x = 224 - 32x2
x2 = 7
x = \(\sqrt{7}\)
= 2.5
= 2\(\frac{1}{2}\)k