The difference between three-fourths and three fifths of a number is 9. Determine the number.
3/4 = .75
3/5 = .6
.75x - .6x = 9
.15x = 9
continue
To find the number, let's set up an equation based on the given information:
Let the number be x.
According to the given information, the difference between three-fourths (3/4) and three fifths (3/5) of the number is 9, which can be written as:
(3/4)x - (3/5)x = 9
To simplify, let's find a common denominator for 4 and 5, which is 20. Rewriting the equation:
(15/20)x - (12/20)x = 9
Now we can subtract:
(15 - 12)/20 * x = 9
(3/20)x = 9
To isolate x, we divide both sides of the equation by (3/20):
x = 9 / (3/20)
To divide by a fraction, we multiply by the reciprocal:
x = 9 * (20/3)
Simplifying the expression:
x = 180/3
x = 60
Therefore, the number is 60.
To determine the number, let's break down the problem step by step:
Step 1: Assign a variable to represent the number
Let's say the number is x
Step 2: Calculate three-fourths of the number
Three-fourths of a number can be calculated by multiplying the number by 3/4, or 0.75.
So, (3/4) * x = (0.75) * x
Step 3: Calculate three-fifths of the number
Three-fifths of a number can be calculated by multiplying the number by 3/5, or 0.6.
So, (3/5) * x = (0.6) * x
Step 4: Set up the equation
According to the problem, the difference between the two calculations is 9. Therefore, we can set up the equation as follows:
(0.75) * x - (0.6) * x = 9
Step 5: Solve the equation for x
Now we can solve the equation to find the value of x:
0.75x - 0.6x = 9
0.15x = 9
x = 9 / 0.15
x = 60
Hence, the number is 60.