SOLUTION: three times the smaller of 2 numbers increased by 5 times the larger is 229. four times the smaller decreased by 25 equals 3 times the larger. find the numbers. Also to solve it

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Question 235993: three times the smaller of 2 numbers increased by 5 times the larger is 229. four times the smaller decreased by 25 equals 3 times the larger. find the numbers.
Also to solve it, we either need to use substitution or elimination method.
Answer by solver91311(5072) About Me  (Show Source):
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Let represent the smaller number. Let represent the larger.

Three times the smaller () increased by () 5 times the larger () is (=) 229.



Call that Equation 1, then



Put the second equation into standard form, that is



And call that equation 2. Multiply equation 1 by 3 and equation 2 by 5:





Notice that the multiplication factors were chosen so that the coefficients on the terms are additive inverses. Add the like terms in the two equations, eliminating the term:



Solve for



Substitute back into either original equation:







Check:



You do the check arithmetic.


John