The sum of the digit of A three digit number is 20 .the middle digit is equal to one fourth the sum of the other two. If the order of the digi be reversed the number increases the original number by woo .find the original number
If the number is abc, then you are told
a+b+c = 20
b = (a+c)/2
100c+10b+a = 100a+10b+c + woo
Now just solve for a,b,c
749
To find the original number, we need to analyze the given conditions step by step.
Let's assume the original three-digit number is represented as ABC, where A represents the hundreds digit, B represents the tens digit, and C represents the ones digit.
1. The sum of the digits of the three-digit number is 20.
This can be represented as: A + B + C = 20.
2. The middle digit is equal to one-fourth of the sum of the other two digits.
This can be represented as: B = (A + C) / 4.
3. Reversing the order of the digits increases the original number by 100A + 10B + C.
The reversed number will be CAB, and the increase can be represented as: 100A + 10B + C - (100C + 10A + B) = 100A + 10B + C - 100C - 10A - B = 99A + 9B - 99C = 99(A - C) + 9(B + C) = 200.
Now, we will solve these equations to find the values of A, B, and C, which will give us the original number.
From the first equation A + B + C = 20, we can rewrite it as A + C = 20 - B and substitute it in the second equation:
B = (A + C) / 4
B = (A + (20 - B)) / 4
4B = A + 20 - B
5B = A + 20
Similarly, from the third equation, we can rewrite it as:
99(A - C) + 9(B + C) = 200
11(A - C) + B + C = 22
11(A - 20 + B) + B + 20 = 22
11A - 220 + 11B + B = 22
11A + 12B = 242
We now have two equations and two variables; we can solve this system of equations using substitution or elimination method. Let's use the substitution method:
From the equation 5B = A + 20, we can rewrite it as A = 5B - 20.
Substituting this value in the equation 11A + 12B = 242:
11(5B - 20) + 12B = 242
55B - 220 + 12B = 242
67B = 462
B = 6
Substituting this value of B back into A = 5B - 20:
A = 5(6) - 20
A = 10
Now, we can substitute the values of A and B into the equation A + B + C = 20:
10 + 6 + C = 20
C = 4
Therefore, the original three-digit number is 106.
Hope this helps!