The population of a village is (x + 5). Each family of the village donated equal
amount for the construction of a school in the village. The total amount collected is
Rs (x4 – 625). Find the amount contributed by each family.
Answers
Given :-
• The population of a village is (x + 5).
• Each family of the village donated equal amount for the construction of a school in the village.
• The total amount collected is
Rs. (x⁴ -625).
To find :-
• The amount contributed by each family.
Solution :-
Given that
The population of a village = (x + 5)
If Each family of the village donated equal amount for the construction of a school in the village.
Let the contribution of each family be Rs.M
Total contribution of the population
= Rs. M × (X+5)
According to the given problem
The total amount collected from the village =
Rs. (x⁴ - 625)
Therefore, M × (x+5) = x⁴ - 625
=> M × (x+5) = (x²)² - (25)²
=> M × (x+5) = (x²+25)(x²-25)
Since, (a+b)(a-b) = a²-b²
Where, a = x² and b = 25
=> M × (x+5) = (x²+25)(x²-5²)
=> M × (x+5) = (x²+25)(x+5)(x-5)
Since, (a+b)(a-b) = a²-b²
Where, a = x and b = 5
=> M = (x²+25)(x+5)(x-5) / (x+5)
=> M = (x²+25)(x-5) or
=> M = x²(x-5) +25(x-5)
=> M = x³-5x²+25x-125
Therefore, M = Rs. (x²+25)(x-5) or
Rs. (x³-5x²+25x-125)
Answer :-
The amount contributed by each family in the village is Rs. (x²+25)(x-5) or Rs.(x³-5x²+25x-125)
Answer:
total population=(x+5)
let donation by each family =y
total amount= (x⁴-625)
therefore y × (x+5) = (x⁴-625)
on solving the value of y comes out to be (x-5)(x²+25)
hence the donation by each family = (x-5)(x²+25)
