A number consists of 3 digits whose sum 9,when digits are reversed, the number decreased by 198 .the
number is ...?
thanks
If the digits are a,b,c
a+b+c=9
100a+10b+c - 198 = 100c+10b+a
The numbers 351, 432 and 513 all work
To solve this problem, we need to make use of algebra and basic arithmetic operations. Let's break down the information given:
1. "A number consists of 3 digits whose sum is 9": This means that the three digits of the number add up to 9. Let's call these digits x, y, and z.
2. "When digits are reversed, the number decreased by 198": This means that when we reverse the order of the three digits, the resulting number is 198 less than the original number.
Now, let's represent the original number as 100x + 10y + z (since it has three digits). When we reverse the digits, the resulting number is 100z + 10y + x. According to the given information, we can set up the following equation:
(100x + 10y + z) - (100z + 10y + x) = 198
Simplifying this equation, we get:
99x - 99z = 198
x - z = 2
We also know that the sum of the three digits is 9:
x + y + z = 9
To solve these two equations simultaneously, we can perform substitution. From the second equation, we can rewrite:
x = 9 - y - z
Substituting this value of x into the first equation, we have:
(9 - y - z) - z = 2
9 - y - z - z = 2
9 - 2z - y = 2
Rearranging terms, we get:
-y - 2z = 2 - 9
-y - 2z = -7
Simplifying further, we have:
y + 2z = 7
Now, we can solve these last two equations simultaneously. We'll use trial and error for the values of y and z. By substituting different values, we find that y = 2 and z = 5 satisfy both equations:
y + 2z = 2 + 2*5 = 12
x + y + z = 9 - 2 - 5 = 2
So, the digits of the original number are 2, 2, and 5. Therefore, the number is 225.