An employer finds that if he increases the weekly wages of each worker by five and employer five worker less he increases his weekly wages bill from 3150 to 3250. Taking the original weekly wage of each work er as ₹x obtain an equation in and then solve it to find weekly wages of each work
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let number of employee initially be n
wage of one employee = x
weekly wages = nx = 3150
n = 3150/x
now
new wage per employee = x + 5
no. of employee = (n - 5)
weekly wages = 3250
(n-5)(x+5) = 3250
nx + 5n - 5x - 25 = 3250
3150 + 5n - 5x - 25 = 3250
5n - 5x = 3250 - 3150 + 25
5n - 5x = 125
n - x = 25
3150/x - x = 25
3150 - x^2 = 25x
x^2 + 25x - 3150 = 0
3150 = 5 x 3 x 7 x 2 x 5 x 3
= 5*3*3 x 5*2*7
= 45*70 (70-45 = 25)
x^2 + 70x - 45x - 3150 = 0
x(x + 70) - 45(x + 70) = 0
(x + 70)(x - 45) = 0
x = 45, -70
wage cannot be negative
hence, x = 45
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