*the sum of 5% of one number and 4% of a second number is 44. the sum of 4% of the first number and 5% of the second number is 46. find the numbers.

The sum of 5% of one number and 4% of a second number is 44. 
The sum of 4% of the first number and 5% of the second number is 46. Find the numbers.

 

0.05*x + 0.04*y = 44, (1) 0.04*x + 0.05*y = 46. (2) Multiply everything by 100. You will get 5*x + 4*y = 4400, (1') 4*x + 5*y = 4600. (2') Add (1') and (2') and divide by 9. You will get x + y = 1000. (3) Distract (2') from (1'). You will get x - y = -200. (4) Next, add (3) and (4) to get 2x = 1200, x = 600. Now from (3) y = 1000 - 600 = 400.