Question 94894: The sum of two numbers is 31. Twice the lesser number is 6 less than twice the greater number. What are the numbers?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let L represent the lesser number and G represent the Greater.
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The sum of these two numbers equals 31. In equation form this is:
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L + G = 31 <=== remember this first equation
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Twice the lesser number (L) plus 6 equals twice the greater number (G). In equation form
this is:
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2L + 6 = 2G <=== this is the second equation
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From the first equation we can solve for L by subtracting G from both sides. When you subtract
G from both sides of the first equation the result is given by:
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L = 31 - G
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In the second equation you can substitute 31 - G in place of L. The second equation then
becomes:
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2(31 - G) + 6 = 2G
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Do the distributed multiplication on the left side by multiplying 2 times 31 and 2 times -G
to get:
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62 - 2G + 6 = 2G
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Get rid of the -2G on the left side by adding 2G to both sides. When you do that the equation
becomes:
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62 + 6 = 4G
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Add the two numbers on the left side:
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68 = 4G
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Solve for G by dividing both sides of this equation by 4 (the multiplier of G) and get:
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68/4 = G
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Dividing 68 by 4 results in 17 and the equation is then:
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G = 17
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We now know that the greater number is 17, and since the two numbers add to 31, the lesser
number L must be 31 - 17 = 14.
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So the two numbers are 17 and 14
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Check: twice the lesser number is 2 times 14 or 28. Is this 6 less than twice the greater
number or 2 times 17 = 34. Yes, 28 is 6 less than 34. Our answers check. The two numbers are
14 and 17.
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Hope this helps you to understand the problem.
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