14 is added to ⅔ of a number. The result is 1¼ times the original number. Find the number.
14 + 2/3 x = 5/4 x
x=12
Answer
To find the number, let's break down the information given in the problem:
Step 1: Start with the unknown number.
Let's assume the unknown number is "x."
Step 2: ⅔ of the number.
The expression "⅔ of a number" can be written as (2/3) * x.
Step 3: Add 14 to ⅔ of the number.
The expression "14 is added to ⅔ of a number" can be written as (2/3) * x + 14.
Step 4: The result is 1¼ times the original number.
The expression "the result is 1¼ times the original number" can be written as 1.25 * x.
Now we can set up the equation using the information we have:
(2/3) * x + 14 = 1.25 * x
To solve for x, we'll isolate the variable on one side of the equation:
(2/3) * x - 1.25 * x = -14
Combine the like terms:
(-2/3 + 1.25) * x = -14
Calculate the values inside the parentheses:
(-0.4167) * x = -14
Divide both sides of the equation by (-0.4167):
x = -14 / (-0.4167)
Using a calculator, the approximate value of x is 33.59.
Therefore, the number is approximately 33.59.