Respuesta :
Answer:
The final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.
Step-by-step explanation:
General Formula
A way to solve this problem is as follows:
The general formula for this is taking into account that:
[tex] \\ percent\;change = \frac{change}{starting\;point}[/tex]
The starting point is number 784.
The most important key is the solution for this answer is that:
[tex] \\ change = starting\;point - x[/tex]
Where x is a number that we need to find. Then
[tex] \\ percent\;change = \frac{starting\;point - x}{starting\;point}[/tex] [1]
Is 784 increased or decreased after all?
We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.
Finding the result
If 784 increases by 3%, we have:
[tex] \\ 3\% = \frac{784 - x}{784}[/tex]
Which is equal to
[tex] \\ 0.03 = \frac{784 - x}{784}[/tex]
Solving for x, we first multiply by 784 to both sides of the previous formula:
[tex] \\ 0.03 * 784 = \frac{784 - x}{784}*784[/tex]
[tex] \\ 0.03 * 784 = (784 - x)*\frac{784}{784}[/tex]
[tex] \\ 0.03 * 784 = (784 - x)*1[/tex]
[tex] \\ 0.03 * 784 = (784 - x)[/tex]
Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.
Subtracting 784 to both sides:
[tex] \\ (0.03 * 784) - 784 = (784 - 784 - x)[/tex]
[tex] \\ (0.03 * 784) - 784 = (0 - x)[/tex]
[tex] \\ (0.03 * 784) - 784 = - x[/tex]
[tex] \\ 23.52 - 784 = - x[/tex]
[tex] \\ -760.48 = - x[/tex]
Multiplying by -1 to both sides:
[tex] \\ -1 * (-760.48) = -1 * (-x)[/tex]
We have to remember that:
[tex] \\ +*+ = +; - * - = +; - * + = -; + * - = -[/tex]
[tex] \\ 760.48 = x[/tex]
Then
[tex] \\ x = 760.48[/tex]
Therefore, using formula [1], an increase of 3% is
[tex] \\ 3\% = \frac{784 - 760.48}{784}[/tex]
[tex] \\ change = 784 - 760.48[/tex]
[tex] \\ change = 23.52[/tex]
Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.
As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.
In a more terse way of solving this problem, we can say that:
Increase of 4% = 784 * 0.04 = 31.36.
Decrease of 1% = 784 * 0.01 = 7.84.
Difference = 31.36 - 7.84 = 23.52.
Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).
