The sum of two different positive integers is 123.
The larger integer is four more than six times the smaller one. What are the two integers?
Let x = the smaller integer.
x + (6x + 4) = 123
7x + 4 = 123
7x = 119
x = ?
Whats the answer
Let's break down the problem step by step to find the two integers.
Let's suppose the smaller integer is represented by 'x'.
The larger integer is then represented by '6x + 4' (since it is four more than six times the smaller integer).
According to the problem, the sum of the two integers is 123. So, we can write the equation as:
x + (6x + 4) = 123
To solve this equation, we need to simplify and combine like terms:
x + 6x + 4 = 123
7x + 4 = 123
Next, we'll isolate the variable by subtracting 4 from both sides:
7x = 123 - 4
7x = 119
Now, we can solve for x by dividing both sides by 7:
x = 119 / 7
x = 17
So, the smaller integer is 17.
To find the larger integer, we substitute the value of x back into our expression '6x + 4':
6(17) + 4 = 102 + 4 = 106
Therefore, the two integers are 17 and 106.