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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-> 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(52776) (Show Source):
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.
