Original Number

harpazo

Pure Mathematics
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One of the digits of a two-digit number is twice the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 99. What is the original number?

What is the set up?
 

MarkFL

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Let one digit be A and the other would then be 2A. Right away we know \(1\le A\le4\). Anyway, using the information in the problem, we can write:

\(\displaystyle (10A+2A)+(20A+A)=99\)

Combine like terms, and solve for \(A\). Because the problem is not specific about which digit is which in the original problem, you have two options for the original number.
 
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harpazo

Pure Mathematics
Banned
Mar 20, 2018
5,788
361
83
NYC
Let one digit be A and the other would then be 2A. Right away we know \(1\le A\le4\). Anyway, using the information in the problem, we can write:

\(\displaystyle (10A+2A)+(20A+A)=99\)

Combine like terms, and solve for \(A\). Because the problem is not specific about which digit is which in the original problem, you have two options for the original number.
Where did 10A and 20A come from?
 

MarkFL

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harpazo

Pure Mathematics
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Mar 20, 2018
5,788
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83
NYC

MarkFL

La Villa Strangiato
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Jan 25, 2018
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St. Augustine
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harpazo

Pure Mathematics
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Mar 20, 2018
5,788
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83
NYC

MarkFL

La Villa Strangiato
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Yes but???
But what? If a number has the two digits from left to right as x and y, then the value of the number (assuming base 10) is 10x + y. If y is twice x, then the number's value is 10x + 2x. Switching the digits gives the number a value of 20x + x.

Does that make sense?
 
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harpazo

Pure Mathematics
Banned
Mar 20, 2018
5,788
361
83
NYC
But what? If a number has the two digits from left to right as x and y, then the value of the number (assuming base 10) is 10x + y. If y is twice x, then the number's value is 10x + 2x. Switching the digits gives the number a value of 20x + x.

Does that make sense?
You said:

"If y is twice x, then the number's value is 10x + 2x. Switching the digits gives the number a value of 20x + x."

How does switching the digits yield
20x + x?
 

MarkFL

La Villa Strangiato
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10(2x) + x = 20x + x.
 
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