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

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

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