- Thread starter harpazo
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\(\displaystyle (10A+2A)+(20A+A)=99\)

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?

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

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.

A two digit number \(AB\) in base ten notation has a value of \(10A+B\).Where did 10A and 20A come from?

I did not know this, honestly.A two digit number \(AB\) in base ten notation has a value of \(10A+B\).

Sure you do...you know that the number \(54\) has a value of \(5\cdot10+4\), right?I did not know this, honestly.

Yes but???Sure you do...you know that the number \(54\) has a value of \(5\cdot10+4\), right?

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.Yes but???

Does that make sense?

You said: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?

"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?