Question

I need step by step explanation for this!!

Answer 1

Answer:  The original number is 57

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Explanation:

T = tens digit of original number

U = units digit of original number

"units digit" is the same as "ones digit"

The original number is in the form 10T+U. For example, let's say that T = 3 is the tens digit and U = 1 is the units digit. This means 10T+U = 10*3+1 = 31 is the original number. Though in this example, the digits don't add to 12.

To make the digits add to 12, we have the equation T+U = 12. This solves to U = 12-T which we'll use later.

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The digits are reversed to get the new number 10U+T and this is 15 times the original tens digit, so

new number = 15*(original tens digit)

10U+T = 15T

from here we plug in U = 12-T which we found earlier. This effectively eliminates or gets rid of the U variable to leave us with T only

10U+T = 15T

10(12-T)+T = 15T ..... replace U with 12-T

which we can now solve for T

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10(12-T)+T = 15T

120-10T+T = 15T

-9T+120 = 15T

120 = 15T+9T ... adding 9T to both sides

120 = 24T

24T = 120

T = 120/24 .... divide both sides by 24

T = 5

The original tens digit is T = 5

The original units digit is U = 12-T = 12-5 = 7

So the original number is 10T+U = 10*5+7 = 57

Flipping the digits gets us 75 which is 15 times that of the original tens digit of 5. The original number has its digits add to 5+7 = 12. The answer has been confirmed.

Answer 2

The original number would be 57