document.write( "Question 568330: the sum of two number is 55 4 times the smaller is 5 less than the larger. Find the numbers? \n" ); document.write( "
Algebra.Com's Answer #366940 by bucky(2189)\"\" \"About 
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Let S represent the smaller number and let L represent the larger.
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\n" ); document.write( "The first sentence in the problem tells you that the sum of the two numbers is 55. In equation form this is:
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\n" ); document.write( "S + L = 55
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\n" ); document.write( "And that is one equation that we can use. Since there are two unknowns we need at least two independent equations to solve for both numbers.
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\n" ); document.write( "The second sentence in the problem tells you that 4 times the smaller (that is 4S) is 5 less than the larger (that is L). Since 4S is 5 less than the larger, you would need to add 5 to 4S to have it equal to L. In equation form this is:
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\n" ); document.write( "4S + 5 = L
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\n" ); document.write( "And this is the second equation that we can use. From this second equation we know what L equals in terms of S. L equals 4S + 5. So we can go to the first equation and in it replace the L with its equal of 4S + 5. When we do that, the first equation is changed to:
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\n" ); document.write( "S + 4S + 5 = 55
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\n" ); document.write( "Add the two terms that contain S and this equation becomes:
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\n" ); document.write( "5S + 5 = 55
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\n" ); document.write( "Get rid of the 5 on the left side by subtracting 5 from both sides to get:
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\n" ); document.write( "5S + 5 - 5 = 55 - 5
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\n" ); document.write( "On the left side the +5 and -5 cancel each other, and on the right side the 55 minus 5 results in 50. So this equation is simplified to:
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\n" ); document.write( "5S = 50
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\n" ); document.write( "You can now solve for the smaller number, S, by dividing both sides by 5, the multiplier of the S term. Dividing the 5S on the left side by 5 you reduce the left side to just S. And dividing the 50 on the right side by 5, the right side becomes just 10. So the equation now shows:
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\n" ); document.write( "S = 10
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\n" ); document.write( "The smaller of the two numbers is 10. But the sum of the two numbers equals 55. So the larger of the two numbers must be 45 so that:
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\n" ); document.write( "10 + L = 55
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\n" ); document.write( "and by subtracting 10 from both sides the larger number L becomes:
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\n" ); document.write( "L = 55 - 10 = 45
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\n" ); document.write( "In summary, the two numbers that are the answer to the problem are 10 and 45.
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\n" ); document.write( "You can see that L + S = 55. And you can also check by seeing that 4S + 5 = L because 4 times 10 is 40 and adding 5 to that makes it 45, and that is equal to the value of L.
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\n" ); document.write( "I hope that this discussion helps you to understand a little more how problems such as this one can be solved.
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