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To solve this problem, you need to begin by finding two equations.
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\n" ); document.write( "First, let's let F represent the first number and S represent the second number.
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\n" ); document.write( "The first sentence of the problem tells you that if you add these two numbers, the sum is 89.
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\n" ); document.write( "F + S = 89
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\n" ); document.write( "That's one equation. The you are told that adding 4 times the first (or 4F) to the second (or S)
\n" ); document.write( "gives 155. So you get the second equation by adding these quantities as follows:
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\n" ); document.write( "4F + S = 155
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\n" ); document.write( "You can't solve a linear equation by itself if it contains two unknowns. Therefore, you
\n" ); document.write( "need to figure out a way of eliminating one of the unknowns in one of the equations.
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\n" ); document.write( "Suppose you go to the first equation and you subtract F from both sides. This results in:
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\n" ); document.write( "F + S - F = 89 - F
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\n" ); document.write( "On the left side the F and the -F cancel each other and you are left with the equation:
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\n" ); document.write( "S = 89 - F
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\n" ); document.write( "Next, go to the second equation:
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\n" ); document.write( "4F + S = 155
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\n" ); document.write( "You now know that S = 89 - F so you can substitute 89 - F for S in the second equation to
\n" ); document.write( "get:
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\n" ); document.write( "4F + 89 - F = 155
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\n" ); document.write( "This new equation only has one variable ... F ... so you can solve it.
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\n" ); document.write( "On the left side, combine the 4F and the -F to get 3F. This reduces the equation to:
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\n" ); document.write( "3F + 89 = 155
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\n" ); document.write( "Then get rid of the 89 on the left side by subtracting 89 from both sides and you have:
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\n" ); document.write( "3F = 66
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\n" ); document.write( "Solve for F by dividing both sides by 3 and the result is:
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\n" ); document.write( "F = 66/3 = 22
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\n" ); document.write( "So now you know that F = 22. You can then return to either of the original equations,
\n" ); document.write( "substitute 22 for F, and solve for S. Let's go back to the first equation:
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\n" ); document.write( "F + S = 89
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\n" ); document.write( "Substitute 22 for F and this equation becomes:
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\n" ); document.write( "22 + S = 89
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\n" ); document.write( "Solve for S by subtracting 22 from both sides:
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\n" ); document.write( "S = 89 - 22 = 67
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\n" ); document.write( "So the answer is that the 2 numbers are 22 and 67.
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\n" ); document.write( "You can further check by substituting these numbers into the original second equation.
\n" ); document.write( "When you do you get:
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\n" ); document.write( "(4*22) + 67 = 88 + 67 = 155
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\n" ); document.write( "and this is what the second part of the problem tells you it should be. Therefore,
\n" ); document.write( "the first number of 22 and the second number of 67 check out. This answer is correct.
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\n" ); document.write( "Hope this helps you to work your way through the problem and understand it a little better.
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