Three-fifth of a certain number is added to two whole number one over two. The result is equal to one whole number one over fiur subtracted from two over there of the number, find the number
Let's represent the certain number as x.
Three-fifth of the number is 3/5 * x.
Adding two whole number one over two to three-fifth of the number is 2 + 1/2 + 3/5 * x.
One whole number one over four is 1 + 1/4 = 5/4.
Two over there of the number is 2/3 * x.
Subtracting one whole number one over four from two over there of the number is 2/3 * x - 5/4.
We have the equation:
2 + 1/2 + 3/5 * x = 2/3 * x - 5/4.
Multiplying the equation by 60 (the least common multiple of 2, 3, 5, and 4), we get:
60 * (2 + 1/2 + 3/5 * x) = 60 * (2/3 * x - 5/4).
Simplifying both sides, we have:
120 + 30 + 36x = 40x - 75.
Combining like terms, we have:
150 + 36x = 40x - 75.
Subtracting 36x and adding 75 to both sides, we get:
150 = 4x - 75.
Adding 75 to both sides, we get:
225 = 4x.
Dividing both sides by 4, we get:
x = 56.25.
Therefore, the number is 56.25.
To find the number, let's break down the given information into equations step by step.
Let's assume the unknown number is "x."
1. "Three-fifths of a certain number is added to two whole number one over two." can be written as:
(3/5)x + 2 1/2
2. "The result is equal to one whole number one over four subtracted from two over there of the number." can be written as:
(2/3)x = 1 1/4
Now, let's solve these equations step by step:
Step 1: Solve for (3/5)x + 2 1/2
(3/5)x + 2 1/2 = (2/3)x - 1 1/4
Step 2: Convert the mixed numbers to improper fractions
(3/5)x + 5/2 = (2/3)x - 5/4
Step 3: Get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators
Multiply by 60 to get rid of denominators:
60 * [(3/5)x + 5/2] = 60 * [(2/3)x - 5/4]
Simplify:
36x + 150 = 40x - 75
Step 4: Solve for "x" by isolating the variable term
36x - 40x = -75 - 150
Simplify:
-4x = -225
Step 5: Solve for "x" by dividing both sides by -4
x = (-225)/(-4)
Simplify:
x = 56.25
Therefore, the number is 56.25.
Let's break down the problem step-by-step:
Step 1: Let's represent the unknown number as "x".
Step 2: Three-fifths of the number "x" can be expressed as (3/5)x.
Step 3: Adding two and a half (two whole numbers and a half) to (3/5)x, we get:
(3/5)x + 2 + 1/2
Step 4: The result is equal to one and a quarter (one whole number and a quarter) subtracted from two-thirds of the number "x". This can be expressed as:
(2/3)x - (1 + 1/4)
Step 5: Equate the expressions obtained in Step 3 and Step 4:
(3/5)x + 2 + 1/2 = (2/3)x - (1 + 1/4)
Step 6: Simplify the equation by removing fractions:
Multiply the entire equation by the least common denominator (LCD) of 30 to eliminate the fractions. (The LCD is 30 because it is the lowest multiple of 5, 2, 3, and 4. )
30 * [(3/5)x + 2 + 1/2] = 30 * [(2/3)x - (1 + 1/4)]
Simplifying this equation, we get:
18x + 60 + 15 = 20x - (30 + 7.5)
18x + 75 = 20x - 37.5
Step 7: Move the variables to one side and constants to the other side:
18x - 20x = -37.5 - 75
-2x = -112.5
Step 8: Solve for "x":
Dividing both sides of the equation by -2, we get:
x = (-112.5) / (-2)
x = 56.25
Therefore, the number is 56.25.
I don't understand. Please can you throw more light on it
Apologies for any confusion. Let's go through the steps again in more detail:
Step 1: Let's represent the unknown number as "x".
Step 2: Three-fifths of the number "x" can be expressed as (3/5)x.
Step 3: Adding two and a half (two whole numbers and a half) to (3/5)x, we get:
(3/5)x + 2 1/2
Step 4: The result is equal to one and a quarter (one whole number and a quarter) subtracted from two-thirds of the number "x". This can be expressed as:
(2/3)x - 1 1/4
Step 5: Equate the expressions obtained in Step 3 and Step 4:
(3/5)x + 2 1/2 = (2/3)x - 1 1/4
Step 6: Simplify the equation by removing fractions:
To do this, we need to find a common denominator for the fractions in the equation.
The common denominator here is 60 because it is the least common multiple of 5, 2, 3, and 4.
Now, multiply every term in the equation by 60:
60 * [(3/5)x + 2 1/2] = 60 * [(2/3)x - 1 1/4]
This simplifies to:
36x + 150 = 40x - 75
Step 7: Move the variables to one side and constants to the other side:
To isolate the variable terms on one side of the equation, let's subtract 36x from both sides and add 75 to both sides:
36x - 36x + 150 + 75 = 40x - 36x - 75 + 75
This simplifies to:
225 = 4x
Step 8: Solve for "x":
Divide both sides of the equation by 4 to solve for "x":
225 / 4 = 4x / 4
This simplifies to:
x = 56.25
Therefore, the number is 56.25.