What is the smaller number of the following:
“The larger of two numbers is twice the smaller number. If 12 is subtracted from the larger number, the result is 7 more than the smaller number.”
7
12
19
26
Let the smaller number be x. According to the given information, the larger number would be 2x.
If 12 is subtracted from the larger number, the result is 7 more than the smaller number:
2x - 12 = x + 7
Subtracting x from both sides gives:
2x - x - 12 = x + x + 7
x - 12 = 2x + 7
Subtracting 2x from both sides gives:
x - 2x - 12 = 7
-x - 12 = 7
Adding 12 to both sides gives:
-x = 7 + 12
-x = 19
Multiplying by -1 gives:
x = -19
Since we are finding the smaller number, it cannot be negative. Therefore, there is no solution to this problem and none of the given options (7, 12, 19, 26) can be the smaller number.
To solve this problem, let's assign variables to the two numbers. Let's call the larger number "L" and the smaller number "S".
According to the problem statement:
"The larger number is twice the smaller number." can be written as L = 2S.
"If 12 is subtracted from the larger number, the result is 7 more than the smaller number." can be written as L - 12 = S + 7.
Now we have a system of two equations:
1. L = 2S
2. L - 12 = S + 7
To find the smaller number, we need to solve this system of equations.
Substituting the value of L from equation 1 into equation 2, we have:
2S - 12 = S + 7
Simplifying the equation:
S - 12 = 7
Adding 12 to both sides of the equation:
S = 19
Therefore, the smaller number is 19.
So the answer is 19.
To find the smaller number, we can set up a system of equations based on the given information.
Let's assume the smaller number is x.
According to the problem, the larger number is twice the smaller number, which can be expressed as 2x.
The second piece of information states that if 12 is subtracted from the larger number (2x - 12), the result is 7 more than the smaller number (x + 7).
Now we can set up an equation based on this information:
2x - 12 = x + 7
To solve for x, we can start by isolating the x term on one side:
2x - x = 7 + 12
x = 19
Therefore, the smaller number is 19.
So, the correct answer is 19.