Answer:
Let's solve each problem step by step.
1. "When 12 is subtracted from three times a number, the answer is equal to two-thirds the number plus 16, find the number."
Let's assume the number is x.
The equation can be written as: 3x - 12 = (2/3)x + 16.
To solve for x, we'll isolate x on one side of the equation.
First, let's get rid of the fraction by multiplying every term in the equation by 3:
3(3x - 12) = 3((2/3)x + 16).
This simplifies to: 9x - 36 = 2x + 48.
Next, we'll move the 2x term to the left side and the -36 term to the right side:
9x - 2x = 48 + 36.
This simplifies to: 7x = 84.
Finally, we'll divide both sides of the equation by 7 to solve for x:
x = 84/7.
Simplifying, we find that x = 12.
Therefore, the number is 12.
2. "If two-thirds of a number is equal to 5, find the number."
Let's assume the number is x.
The equation can be written as: (2/3)x = 5.
To solve for x, we'll isolate x on one side of the equation.
First, let's get rid of the fraction by multiplying every term in the equation by 3/2:
(3/2)(2/3)x = (3/2)(5).
This simplifies to: x = 15/2.
Simplifying further, we find that x = 7.5.
Therefore, the number is 7.5.