Question

a number consists of three digits of each middle one is 0 and some of the Other digit is 9 the number formed by 1 digit is more than the 297 find the number

Answer 1

A number consist of three digits of whose sum is 17 the middle digit exceeds the sum of two digits by one if the digits of the number are reversed the number dimini shes by 396 find the number? 

Let the hundreds, tens, and units digits be H, T, & U, respectively
Since the 3 digits sum to 17, then: H + T + U = 17 ------ eq (i) 

Since the middle digit (T) exceeds the sum of the other 2 digits by 1, then: 
T = H + U + 1
H – T + U = - 1 ---- eq (ii) 

Since when number is reversed the number diminishes by 396, then: 
100U + 10T + H = 100H + 10T + U - 396
H - 100H + 10T – 10T + 100U – U = - 396
– 99H + 99U = - 396 
99(- H + U) = 99(- 4) ----- Factoring out GCF, 99 
- H + U = - 4 ----- eq (iii) 

H + T + U = 17 ---- eq (i)
H – T + U = - 1 ---- eq (ii)
2H + 2U = 16 ----- Adding eqs (i) & (ii)
2(H + U) = 2(8) ------ Factoring out GCF, 2
H + U = 8 ------- eq (iv)
- H + U = - 4 ----- eq (iii)
2U = 4 ----- Adding eqs (iv) & (iii)
U, or units digit = , or  

H + 2 = 8 ----- Substituting 2 for U in eq (iv)
H, or hundreds digit = 8 – 2, or  

6 + T + 2 = 17 ------ Substituting 2 for U, and 6 for H in eq (i)
T = 17 – 8
T, or tens digit =  

The original number is