Question 215408: I am homeschooled with the School of Tomorrow, and am struggling with solving word problems involving two-digit numerals. The question I am having difficulty with now is this: "The value of a two-digit number is twice as large as the sum of its digits. If the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find the original number." Thank you for your help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! "The value of a two-digit number is twice as large as the sum of its digits.
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Equation #1:
10t+u = =2(t+u)
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If the digits were reversed, the resulting number would be 9 less than 5 times the original number.
Equation #2:
10u+t =5(10t+u)-9
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Find the original number."
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Rearrange the two equations:
#1: 8t-u = 0
#2: 49t-5u = 9
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Then:
u = 8t
Substitute for "u" to solve for "t":
49t-5(8t) = 9
9t = 9
t = 1
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Since u = 8t, u = 8
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The original number is 18
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Cheers,
Stan H.
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