How they got by using (1-1/5)x=240 how do they get 1 in the formula
To solve the equation (1-1/5)x=240, we first distribute the coefficient of x, which is (1-1/5)x.
(1-1/5)x = 1x - (1/5)x
Simplifying further, we have:
1x - (1/5)x = (5/5)x - (1/5)x = (5-1)/5 x = (4/5)x
Now, the equation becomes:
(4/5)x = 240
To get rid of the fraction coefficient, we multiply both sides of the equation by the reciprocal of (4/5), which is 5/4:
(5/4) * (4/5)x = (5/4) * 240
On the left side, the 4s cancel out, and on the right side, the 5s cancel out, resulting in:
x = (5/4) * 240
Simplifying the right side:
x = (5 * 240) / 4
Now we solve the right side:
x = 1200 / 4
Simplifying further:
x = 300
Therefore, the value of x that satisfies the equation (1-1/5)x=240 is x = 300.
But the question did not have 1
I apologize for the confusion. To solve the equation (1-1/5)x=240, we do not need to introduce an additional 1 in the equation.
Starting with the original equation:
(1-1/5)x = 240
We can simplify by subtracting 1/5 from 1, which gives us:
(4/5)x = 240
To isolate x, we divide both sides of the equation by 4/5:
(4/5)x / (4/5) = 240 / (4/5)
On the left side, the 4/5 cancels out, and on the right side, we invert the divisor and multiply:
x = 240 * (5/4)
Simplifying the right side:
x = (240 * 5) / 4
Now we solve the right side:
x = 1200 / 4
Simplifying further:
x = 300
Therefore, the value of x that satisfies the equation (1-1/5)x=240 is x = 300.
To understand how the number 1 is derived in the formula (1-1/5)x = 240, let's break down the steps:
Step 1: Start with the given equation: (1-1/5)x = 240.
Step 2: Simplify the equation by subtracting 1/5 from 1. The subtraction is done because there is a negative sign before 1/5.
(1 - 1/5) can be written as (5/5 - 1/5) = (4/5)
Step 3: Rewrite the equation using the simplified term from Step 2:
(4/5)x = 240
Step 4: To solve for x, we need to isolate it on one side of the equation. To do this, we can multiply both sides of the equation by the reciprocal of 4/5, which is 5/4.
By multiplying both sides by 5/4, we eliminate the fraction on the left side, and the equation becomes:
((4/5)x) * (5/4) = 240 * (5/4)
Step 5: Simplify the equation:
(4/5) * (5/4) is equal to 1, because the numerator and denominator cancel each other out. This is why we have 1 multiplied by x (1x).
1x = 240 * (5/4)
Step 6: Simplify the right side of the equation:
240 * (5/4) can be calculated as follows:
240 ÷ 4 = 60
60 * 5 = 300
So, the equation becomes:
1x = 300
Step 7: Simplify further:
Since 1x is equal to simply x, the equation can be written as:
x = 300
Therefore, the value derived from the given equation (1-1/5)x = 240 is x = 300.