document.write( "Question 1131188: The sum of three numbers is 15. The sum of twice the first number, 4 times the second number, and 5 times the third number is 49. The difference between 3 times the first number and the second number is 16. Find the three numbers. \n" ); document.write( "

Algebra.Com's Answer #747820 by MathTherapy(10551) $\"\"$ $\"About$

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\n" ); document.write( "The sum of three numbers is 15. The sum of twice the first number, 4 times the second number, and 5 times the third number is 49. The difference between 3 times the first number and the second number is 16. Find the three numbers.
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Let 1st, 2nd, and 3rd numbers be F, S, and T, respectively
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document.write( "Then we get: 
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document.write( "F + 3F - 16 + T = 15 ------ Substituting 3F - 16 for S in eq (i)
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document.write( "4F + T = 31 ------ eq (iv)\r
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document.write( "2F + 4(3F - 16) + 5T = 49 -- Substituting 3F - 16 for S in eq (ii)
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document.write( "14F + 5T = 113 ------------- eq (v)
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document.write( " - 20F - 5T = - 155 -------- Multiplying eq (iv) by - 5 ------ eq (vi)
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document.write( " - 6F = - 42 --------------- Adding eqs (vi) & (v)
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