A two digit positive number is such that the ones digit is 2.5 as much as the tens digit. If the difference between the number and the number obtained when the digits are reversed is 27 , find the number.
Straight from my 7th grade textbook!
Answers
A two digit positive number is such that the ones digit is 2.5 as much as the tens digit. If the difference between the number and the number obtained when the digits are reversed is 27 , find the number.
Answer:
Step-by-step explanation: 10x + 2.5x = 12.5x = number
10x + x = 11x = number when digits are reversed
The difference between the two numbers is 11x - 12.5x = -1.5x. We are given that this difference is equal to 27, so we can set up the following equation:
-1.5x = 27
x = -18
The tens digit is -18, so the two-digit number is 10(-18) + 2.5(-18) = -180 + (-45) = -225. However, this is not a positive two-digit number.
If we try the next smallest value for x, -17, the two-digit number is -170 + (-42.5) = -212.5, which is not a positive two-digit number.
The only remaining possibility is that x = -16. In this case, the two-digit number is -160 + (-40) = -200, which is equal to 25 when the digits are reversed. Therefore, x = -16 and the two-digit number is 25.
I hope this helps!