one person bought some sugar in rs 80 .if he would get 4 kg more sugar with that money ,then the price of 1 kg sugar would be less by 1. construct the quadratic eqation in one variable
Answers
Answer:
(80/x+4)-1=1kg
Step-by-step explanation:
The quadratic eqation in one variable is x² + 4x - 320 = 0, and the quantity of rice bought = 16 kg.
• Let the quantity of sugar bought be x kg.
Given that, price at which he bought x kg of sugar = Rs. 80
=> Price of 1 kg sugar = Rs. 80 / x
• If he buys 4 kg more sugar, the quantity becomes (x + 4) kg.
It is given that he buys (x + 4) kg of sugar with the same money.
New price of each kg of sugar = 80 / (x + 4)
• Also given that, new price of each kg of sugar reduces by 1 rupee.
=> New price of each kg of sugar = (80 / x) - 1
= (80 - x) / x
• According to the question,
80 / (x + 4) = (80 - x) / x
On cross-multiplying, we get,
=> 80x = (80 - x) (x + 4)
=> 80x = 80x + 320 - x² - 4x
Bringing all the terms on left hand side,
=> 80x - 80x - 320 + x² + 4x = 0
=> - 320 + x² + 4x = 0
=> x² + 4x - 320 = 0 (The required quadratic equation)
=> x² + 20x - 16x - 320 = 0
=> x (x + 20) - 16 (x + 20) = 0
=> (x - 16) (x + 20) = 0
=> x - 16 = 0 ; x + 20 = 0
=> x = 16 ; x = - 20
• Since quantity cannot be negative, x = - 20 is discarded.
Therefore, the quantity of rice bought by the person = 16 kg