SOLUTION: Four times a certain number increased by three times a second number is 25. Four times the first number decreased by three times the second number is 7. Find the two numbers.

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Question 1101958: Four times a certain number increased by three times a second number is 25. Four times the first number decreased by three times the second number is 7. Find the two numbers.
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
4x + 3y = 25,     (1)
4x - 3y =  7.     (2)
---------------------------Subtract eq(2) from eq(1). You will get

6y = 25 - 7 = 18  ===>  y =  = 3.


Then from (1),  4x = 25 - 3y = 25 - 3*3 = 25 - 9 = 16;


Hence, x =  = 4.


Answer.  First number is  4;  second number is  3.

The good style in solving such problems is to notice/(to observe) immediately from the condition that the difference
between two combinations is 6 times the second number, which, in turn, is the difference 25-7 = 18,
and to deduce from it MENTALLY that y= 3, without writing any equations.

This problem is for mental solution, and it would be ideally if you see the solution immediately/instantly.


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