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Answer: The original number is 57</h3>
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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.
