document.write( "Question 1198673: Use a system of equations to solve the following problem\r
\n" ); document.write( "\n" ); document.write( "The sum of 3 integers is 314. The sum of the first and second integers exceeds the third by 40. The third integer is 26 less than the first. Find the three integers. \n" ); document.write( "
Algebra.Com's Answer #832300 by math_tutor2020(3821)\"\" \"About 
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\n" ); document.write( "x = first integer
\n" ); document.write( "y = second integer
\n" ); document.write( "z = third integer
  • Fact 1: The sum of 3 integers is 314.
  • Fact 2: The sum of the first and second integers exceeds the third by 40.
  • Fact 3: The third integer is 26 less than the first.
x+y+z = 314 from fact 1
\n" ); document.write( "x+y = z+40 from fact 2
\n" ); document.write( "z = x-26 from fact 3\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Plug z = x-26 into the first equation
\n" ); document.write( "Then solve for y
\n" ); document.write( "x+y+z = 314
\n" ); document.write( "x+y+x-26 = 314
\n" ); document.write( "2x+y = 340
\n" ); document.write( "y = -2x+340\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's plug those y and z expressions into the second equation and solve for x.
\n" ); document.write( "x+y = z+40
\n" ); document.write( "x+(-2x+340) = x-26+40
\n" ); document.write( "-x+340 = x+14
\n" ); document.write( "-x-x = 14-340
\n" ); document.write( "-2x = -326
\n" ); document.write( "x = -326/(-2)
\n" ); document.write( "x = 163\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Use that to find the second integer
\n" ); document.write( "y = -2x+340
\n" ); document.write( "y = -2*163+340
\n" ); document.write( "y = 14\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Use that to find the third integer
\n" ); document.write( "z = x-26
\n" ); document.write( "z = 163-26
\n" ); document.write( "z = 137\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Summary:
\n" ); document.write( "x = 163
\n" ); document.write( "y = 14
\n" ); document.write( "z = 137\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Check:
  • x+y+z = 163+14+137 = 314 which verifies fact 1
  • x+y = 163+14 = 177 which is 40 larger than z = 137, since 137+40 = 177, confirming fact 2
  • 137 is 26 less than 163 since 163-26 = 137, which confirms fact 3.

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