Question 496781: The larger of two numbers is 3 more then twice the smaller. The difference of the larger number and the smaller number is 8. Find the numbers.
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! This is another way to get students to solve two equations with two unknowns. The first step is to make sure you can turn the words in equations correctly.
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Let L = the larger #
Let S = the smaller #
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The first sentence said L is 3 more than twice S. That is:
L = 2S + 3
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The second sentence said the difference between the larger and smaller is 8, that is:
L - S = 8
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In this case, since one of the equations is already cast as one unknown in terms of the other, we can plug in that identity into the 2nd equation and solve for the one unknown:
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Plug L = 2S + 3 into: L - S = 8, to get:
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(2S + 3) - S = 8
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Group all the S terms on one side of the "=" and all the numerical constants on the other side:
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2S - S = 8 - 3
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Note: we got here by substracting 3 from both sides of the equation.
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2S - S = 8 - 3
S = 5
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Go back to either of the original equations using S = 5 to find L:
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L - (5) = 8
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adding 5 to both sides (to again get the unknown by itself):
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L = 13
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Go back and check you work to make sure both equations are true with S = 5 and L= 13
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cheers,
Lee
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