The sum of two numbers is 46. When 30 is subtracted from 5 times the smaller the result is 3 times the larger. Determine the numbers.

**ANSWER:**

Let x be the smaller number and y be the larger number.

equation 1: x + y = 46 —>—->—->—-> y = 46 – x

equation 2: 5x – 30 = 3y

sub (equation 1) in (equation 2);

5x – 30 = 3y y= 46 -x

5x – 30 = 3( 46 – x) y = 46 – 21

5x – 30 = 138 – 3x y = 25

-30 – 138 = -3x – 5x

-168 = -8x

x = 21

.*. The smaller number is 21 and the **larger number is 25**