A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 be subtracted from it the digits will be reversed. Find the number.
To find the number, let's start by considering the given conditions.
Condition 1: A certain number between 10 and 100 is 8 times the sum of its digits.
Let's assume the number is AB, where A and B are the digits. According to the condition, the number AB is equal to 8 times the sum of its digits: 8(A + B).
Condition 2: If 45 is subtracted from it, the digits will be reversed.
When we subtract 45 from AB, the resulting number should have its digits reversed. Therefore, the resulting number is BA. Mathematically, this can be expressed as: AB - 45 = BA.
Now, let's solve the equations to find the values of A and B.
First, let's simplify the equation AB - 45 = BA. Since A and B represent the digits, we can rewrite the equation as 10A + B - 45 = 10B + A.
Simplifying further, we get 9A - 9B = 45.
Dividing both sides by 9, we have A - B = 5.
Since A and B are digits, the only possibility that satisfies this equation is A = 6 and B = 1.
Therefore, the number AB is 61.
So, the answer is 61.
How you directly write answer
Where is the solution?
72
72
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If the digits are a and b then
10a+b = 8(a+b)
10a+b - 45 = 10b + a
The number is 72