SOLUTION: The difference between a two-digit number and the number obtained by interchanging its digits is 54. If the ratio of the digit at unit's place to the digits at ten 's place is 1:3;
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Question 897351: The difference between a two-digit number and the number obtained by interchanging its digits is 54. If the ratio of the digit at unit's place to the digits at ten 's place is 1:3;what is the difference between the sum and the difference of the digits?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let a = the 10's digit
Let b = the units:
:
The difference between a two-digit number and the number obtained by interchanging its digits is 54.
10a+b -(10b+a) = 54
10a + b - 10b - a = 54
9a - 9b = 54
simplify, divide by 9
a - b = 6
:
If the ratio of the digit at unit's place to the digits at ten 's place is 1:3;
=
cross multiply
a = 3b
In the 1st simplified equation, replace a with 3b
3b - b = 6
2b = 6
b = 3
find a
a = 3(3)
a = 9
:
93 is the number
:
what is the difference between the sum and the difference of the digits?
(a+b) - (a-b)
(9+3) - (9-3)
12 - 6 = 6
:
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