SOLUTION: Find the largest two digit integer that is increased by 75% when it's digits are reversed.

Question 843199: Find the largest two digit integer that is increased by 75% when it's digits are reversed.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let your digits be a and b.

your first number is ab.
your second number is ba.

the value of your first number is 10a + b
the value of your second number is 10b + a.

assume that your second number is 75% bigger than your first number.

this means that your second number is 1.75 times as big as your first number.

since the value of your first number is 10a + b and the value of your second number is 10b + a, this means that:

10b + a is equal to 1.75 * (10a + b)

simplify this equation to get:

10b + a = 17.5 * a + 1.75 * b

subtract 1.75 * b from both sides of this equation and subtract a from both sides of this equation to get:

10b - 1.75b = 17.5a - a

simplify this to get:

8.25b = 16.5a

divide both sides of this equation by 8.5 to get:

b = 16.5a/8.25

this simplifies to b = 2a

since b has to be an integer, and b has to be 2a, then the biggest that b can be is 8.

if it were 9, than a would not be an integer.

it can't be 10 since a single digit can only go up to 9.

so the biggest that b can be is 8 and this means that the biggest that a can be is 4 which is 1/2 * b.

since your first number is ab, then that number is 48.
since your second number is ba, then that number is 84.

84 is 1.75 * 48 so the solution is good.

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