Question

if from twice the greater number of two positive numbers, 16 is subtracted, the result is half the other. if from half the greater number, 1 is subtracted, the result is half the other number. find the numbers

Answer 1

Let the greater number be a and smaller number be b. So - 
1) Twice the greater number is 2a.
2) Subtracting 16 from 2a => 2a-16.
3) This is equal to half the smaller number. => $\frac{1}{2} b = 2a -16$
Multiply both sides by 2, we get - 
b = 4a - 32 -------------------(1)

1) Half the greater number is $\frac{1}{2} a$.
2)Subtracting 1 from a/2 => $\frac{1}{2} a - 1$.
3)This is equal to half the smaller number. =>$\frac{1}{2} b = \frac{1}{2} a - 1$.
Multiply both sides by 2, we get -
=>  b = a -2 --------------------(2)

Subtract (2) from (1),we get

3a - 30 = 0
=> a = 10
Putting a in (1), we get - 
b = 4.a - 32 = 4.10 -32 = 8

=> (a,b) = 10, 8

Bigger number is 10, smaller number is 8.

Answer 2

Hope this helpfull for you