document.write( "Question 1124158: The sum of three numbers is 10. The sum of twice the first number, 4 times the second number, and 5 times the third number is 33. The difference between 6 times the first number and the second number is 19. Find the three numbers.\r
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Algebra.Com's Answer #740535 by MathTherapy(10552) $\"\"$ $\"About$

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\n" ); document.write( "The sum of three numbers is 10. The sum of twice the first number, 4 times the second number, and 5 times the third number is 33. The difference between 6 times the first number and the second number is 19. Find the three numbers.\r
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Let the 1st, 2nd and 3rd numbers be F, S, and T, respectively
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document.write( "Then: F + S + T = 10 --------- eq (i)
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document.write( "Also, 2F + 4S + 5t = 33 ------ eq (ii)
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document.write( "And, 6F - S = 19____S = 6F - 19 ------- eq (iii)
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document.write( "F + 6F - 19 + T = 10_____7F + T = 29______T = 29 - 7F -------- Substituting 6F - 19 for S in eq (i) ------- eq (iv)
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document.write( "2F + 4(6F - 19) + 5T = 33_____2F + 24F - 76 + 5T = 33_____26F + 5T = 109 -------- Substituting 6F - 19 for S in eq (ii) ------- eq (v)
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document.write( "26F + 5(29 - 7F) = 109 ------- Substituting 29 - 7F for T in eq (v)
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document.write( "26F + 145 - 35F = 109
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document.write( "- 9F = - 36
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document.write( "F, or 1st number =  
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document.write( "S = 6(4) - 19 --------- Substituting 4 for F in eq ((iv)
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document.write( "S, or 2nd number = 
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document.write( "T = 29 - 7(4) ------ Substituting 4 for F in eq (iv)
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document.write( "T, or 3rd number =  \n" );
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