One number is 2 more than another number. Add 11 to 6 times the first number. The result is 7 times the second number.
I'm not sure which number is the "first number."
One number = x+2 and the other = x.
6(x+2)+11 = 7x
Solve for x.
Let's break down the problem step by step:
Let's assume the first number is x.
The second number would then be (x + 2) because it is 2 more than the first number.
Now, we're given that if we add 11 to 6 times the first number, or (6x + 11), we get 7 times the second number, or 7(x + 2).
So, we can set up an equation to solve for x:
6x + 11 = 7(x + 2)
To solve this equation, we will distribute 7 to both terms inside the parentheses:
6x + 11 = 7x + 14
Next, let's isolate the x terms by subtracting 6x from both sides:
11 = 7x - 6x + 14
Simplifying further, we have:
11 = x + 14
Now, let's isolate the x term by subtracting 14 from both sides:
11 - 14 = x
-3 = x
Therefore, the first number is -3.
To find the second number, which is 2 more than the first number, we add 2 to x:
Second number = -3 + 2 = -1
So, the second number is -1.
Thus, the first number is -3 and the second number is -1.