Question

The tens digit of a two-digit number is 6 more than the ones digit. If given
If the number is equal to 10 times the sum of the digits, find the original number.​

Answer 1

Answer:

A number with two digits can be written as AB where the A and the B are the digits in the tens and ones places. I set up one of the other questions you asked, I'll solve this one out in case you need to see how it's done.

A = B + 1

AB can be rewritten as 10A + B

10A + B = 6(A + B)

This gives me a system of equations. Since the first equation gives me A in terms of B, I'll replace the As in the second equation with B + 1. The first equation is saying that "A is the same thing as B + 1".

So dealing with the second equation:

10A + B = 6(A + B)

10(B + 1) + B = 6(B + 1 + B)

10B + 10 + B = 6B + 6 + 6B

11B + 10 = 12B + 6

B = 4

Then A is one more than this, so A = 5.

The number is 54.

(Check this: the tens digit is one more than the ones digit. Got that. When I add the digits together I get 9. If I multiply 9 by 6, I get 54.)

Step-by-step explanation:

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