Question
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
“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
Answers
GPT 3.5
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.
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.