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What is an odd two digit number the difference of the two digis its is 5 and the difference in the squares of the two digits is 45?
The number is 27
let the number be xy (that is it is 10x + y). Then:
Assume x is the bigger digit, then
- x - y = 5 ⇒ x = y + 5
- x2 - y2 = 45
Substituting for x in 2 using 1 above:
(y + 5)2 - y2 = 45
⇒ y2 + 10y + 25 - y2 = 45
⇒ 10y = 20
⇒ y = 2
⇒ x = 7
But y must be odd since xy is odd.
If y was assumed to be the bigger digit, x and y would be swapped in the above calculation, thus the values of x and y can be swapped:
x = 2, y = 7 ⇒ the number is 27
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