document.write( "Question 473168: There are 357 calories in two slices of bread and three eggs. There are 217 calories in one slice of bread and two eggs. How many calories are in a slice of bread and how many are in an egg \n" ); document.write( "
Algebra.Com's Answer #324470 by karaoz(32)\"\" \"About 
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The unknown values are:
\n" ); document.write( "- number of calories in a slice of bread
\n" ); document.write( "- number of calories in an egg
\n" ); document.write( "
We can use letters b and e to name these two variables (that way it is easier to remember which one represents what, b for bread and e for egg).
\n" ); document.write( "b = number of calories in a slice of bread
\n" ); document.write( "e = number of calories in an egg

\n" ); document.write( "Translate the relevant information into algebraic statements:
\r\n" );
document.write( "1st sentence: 2b + 3e = 357\r\n" );
document.write( "2nd sentence:  b + 2e = 217\r\n" );
document.write( "3rd sentence:  b = ?, e = ?

\n" ); document.write( "Solve the system:
\r\n" );
document.write( "2b + 3e = 357\r\n" );
document.write( " b + 2e = 217

\n" ); document.write( "Multiply the second equation by (-2) and add the resulting equation to the first one.
\n" ); document.write( "The intention here is to eliminate variable b (because it is easier than to eliminate variable e) and reduce the system from 2 equations with 2 unknowns down to 1 equation with 1 unknown.
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document.write( " (b + 2e =  217) * (-2)\r\n" );
document.write( "----------------------\r\n" );
document.write( "-2b - 4e = -434
\r\n" );
document.write( " 2b + 3e =  357\r\n" );
document.write( "-2b - 4e = -434\r\n" );
document.write( "----------------------\r\n" );
document.write( "    -  e = - 77

\n" ); document.write( "Solve the above equation by multiplying it by (-1)
\r\n" );
document.write( "   (-  e = - 77) * (-1)\r\n" );
document.write( "----------------------\r\n" );
document.write( "       e =   77

\n" ); document.write( "Solved for e. Now solve for b by using the obtained value for e.
\n" ); document.write( "For this purpose, we can use any of the two original equations.
\n" ); document.write( "Let's take the second one since it will be easier to solve for e.
\r\n" );
document.write( " b + 2e    = 217\r\n" );
document.write( " b + 2(77) = 217\r\n" );
document.write( " b + 154   = 217\r\n" );
document.write( " b         = 63

\n" ); document.write( "Solved.

\n" ); document.write( "Number of calories in a slice of bread is 63.
\n" ); document.write( "Number of calories in an egg is 77. \n" ); document.write( "
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