Question

let x, y, and z be positive integers. If x is 12.5% of y and x is 3.125% of z, then x is what percent of y+z?

Answer 1

Step-by-step explanation:

Given :-

let x, y, and z be positive integers and x is 12.5% of y and x is 3.125% of z.

To find :-

Find x is what percent of y+z?

Solution :-

Given that :

x,y and z are positive integers.

x is 12.5% of y

=> x = 12.5% of y

=> x = 12.5%× y

=> x = (12.5/100)×y

=> x = (125/1000)×y

=>x = (1/8)×y

=> x = y/8-------------------(1)

=> x×8 = y

=> y = 8x -------------------(2)

and

x is 3.125% of z

=>x = 3.125% of z

=>x = 3.125% ×z

=> x = (3.125/100)×z

=> x = (3125/100000)×z

=> x = (1/32)×z

=>x = z/32 ----------------(3)

=> x×32 = z

=> z = 32x ------------------(4)

on adding (2) & (4)

=> y+z = 8x+32x

=> y+z = 40x -------------(5)

=> x = (y+z)/40 -----------(6)

Let x be the A% of (y+z)

=>x = A% of (y+z)

=> x = A% ×(y+z)

=> x = (A/100)×(y+z)

=> x = (y+z)×A/100

=> x = (40x)×A/100 (from (5))

=> x = 40xA/100

=> x = 2xA/5

On cancelling X both sides

=> 1 = 2A/5

=> 1×5 = 2A

=> 5 = 2A

=> 2A = 5

=> A = 5/2

=>A = 2.5

Therefore, A= 2.5%

Answer :-

x is 2.5% of (y+z) for the given problem