There is a three digit number. The sum of the three digits is 12. The hundred digit number is 7 times larger than the ten digit number, and the one digit number is 3 times of the ten digit number Solving linear equation with one variable

There is a three digit number. The sum of the three digits is 12. The hundred digit number is 7 times larger than the ten digit number, and the one digit number is 3 times of the ten digit number Solving linear equation with one variable

Suppose ten digit is x, then 100 digit is x + 7, and one digit is 3x
X+X+7+3X=12
The solution is x = 1
So x + 7 = 8
3X=3
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For a three digit number, the sum of the number and the number in the hundreds is equal to the number in the tens, and the number in the hundreds is 7 times greater than the sum of the number in the tens by 2
The sum of the numbers in the tens and hundreds is 14

A hundred, ten, a B C
a+c=b
7a=c+b+2
a+b+c=14
7a=14-a+2
a=2
b-c=2
b+c=14-2=12
b=7
c=5
The number is 275

The sum of a three digit number, a single digit number and a hundred digit number is equal to a ten digit number. Seven times the sum of a hundred digit number is two times larger than that of a single digit number and a ten digit number. The sum of a single digit number, a ten digit number and a hundred digit number is 14

This three digit number is x on the one digit, y on the ten digit, and z.x + Z = y on the hundred digit. ① 7z = x + y + 2x + y + Z = 14. ③ substitute ① into ③ to get y = 7. Substitute y = 7 into ① to get x + z = 7. ④ substitute ② to get 7z = x + 9. ⑤ ④ - ⑤ to get z = 2, ｜ x = 5. This three digit number is 2 × 100 + 7 × 10 + 5 = 275. Answer: this three digit number is 275