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Question 1061260: 2. The digits of a two-digit number differ by 2. If the digits are reversed, the new number is 18 less than the original number. Find the original number.
3. A total of Php500 000 is invested in 3 funds paying 6%, 8% and 10% simple interest rate.The annual income from the three investment is Php37 000. If the amount invested at 6%interest rate is twice as much of that invested in 10% interest rate, and the amount invested at 8% interest rate?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! The digits question
 , the two-digit number.
Try substituting this into the absolute value equation.
 ------------always true.
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START AGAIN TO SOLVE:
Assume  , for t TENS and u ONES.
 , knowing that when digits switched, new number is smaller;
The description is essentially ONE equation in TWO unknown variables.
Solution set:
31, 42, 53, 64, 75, 86, 97, 20
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website!
2. The digits of a two-digit number differ by 2. If the digits are reversed, the new number is 18 less than the original number. Find the original number.
3. A total of Php500 000 is invested in 3 funds paying 6%, 8% and 10% simple interest rate.The annual income from the three investment is Php37 000. If the amount invested at 6%interest rate is twice as much of that invested in 10% interest rate, and the amount invested at 8% interest rate?
Let the tens, and units digits, be T and U, respectively
Since the reversed number is less than the original number, it follows that T will be > U
We then get: T - U = 2 ------- eq (i)
Also, 10U + T = 10T + U – 18_____10T – T + U – 10U = 18_____9T - 9U = 18____9(T - U) = 9(2)_____T - U = 2 ----- eq (ii)
Since both equations are identical, then ANY 2-digit number, with its tens digit being larger than its units digit by 2, and when reversed, results in
another 2-digit number that is 18 less than the original number, WILL WORK!
That’s it….nothing COMPLEX, nothing to write a BOOK on!
BTW, 20 is not one of the original numbers, since when it's reversed, IT'S NOT a 2-digit number, so let no-one tell you otherwise!!
Try # 3. I can't do EVERYTHING for you! How would you learn if I did?
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