4. the larger of two numbers is twice the smaller number. if 12 is subtracted from the larger number, the…

4. 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. find the numbers.

4. 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. find the numbers.

Answer

Explanation:

Step1: Set up variables

Let the smaller number be (x). Then the larger number is (2x).

Step2: Form an equation

According to the problem, (2x - 12=x + 7).

Step3: Solve the equation

Subtract (x) from both sides: (2x-x-12=x - x+ 7), which simplifies to (x-12 = 7). Add 12 to both sides: (x-12 + 12=7 + 12), so (x = 19).

Step4: Find the larger number

Since the larger number is (2x), substitute (x = 19) into it. (2x=2\times19 = 38).

Answer:

The smaller number is (19) and the larger number is (38).