14 Is added to ⅔ of a number. the result is 1¼ times the original number. find the number
(2/3)x + 14 = (1 1/4)x
14 = (1 1/4)x - (2/3}x
14 = (15/12)x - (8/12)x
14 = (7/12)x
14 / (7/12) = x
14 * (12/7) = x
24 = x
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24
Oh, so the number wants to play hide and seek with us, huh? Alright, let's solve this puzzle together!
Let's assume the number we're looking for is "x."
According to the problem, "14 is added to ⅔ of a number." So, we can write the equation as follows:
x/3 + 14 = (5/4) * x
Now, let's simplify this equation step by step. We can start by multiplying both sides of the equation by 4 to get rid of the pesky fractions:
4 * (x/3 + 14) = 4 * (5/4) * x
After simplifying, we have:
4x/3 + 56 = 5x
Next, let's subtract 4x/3 from both sides of the equation:
4x/3 - 4x/3 + 56 = 5x - 4x/3
Simplifying once again:
56 = 5x - 4x/3
Now, let's gather all the x terms together:
56 = (5 - 4/3)x
To simplify further, let's find a common denominator for 4 and 3:
56 = (15/3 - 4/3)x
56 = (11/3)x
Finally, to isolate x, let's divide both sides of the equation by (11/3):
x = 56 / (11/3)
Calculating the division, we find:
x ≈ 15.27
So, the mysterious number we've been searching for is approximately 15.27. Keep in mind, though, that this number may have been hiding, but it didn't forget to leave a decimal trail for us!
To find the number, we can first set up an equation based on the given information.
Let's assume the number is represented by "x".
According to the question, "14 is added to 2/3 of the number." This can be written as:
14 + (2/3)x
The resulting expression is "1¼ times the original number." "1¼ times the original number" can be represented as:
1.25x
Now we can set up the equation:
14 + (2/3)x = 1.25x
Next, we can solve for "x" by isolating it on one side of the equation.
First, let's get rid of the fraction by multiplying the entire equation by 3 to clear the denominator:
3(14 + (2/3)x) = 3(1.25x)
After simplifying, we have:
42 + 2x = 3(1.25x)
42 + 2x = 3.75x
Now, let's isolate the variable "x" on one side of the equation:
42 = 3.75x - 2x
Combine the "x" terms:
42 = 1.75x
To solve for "x", divide both sides of the equation by 1.75:
x = 42 / 1.75
Evaluating the division:
x = 24
Therefore, the number is 24.