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2 years ago

Percent of discount is 25% and the new price is 40$ whats the original price?

Mathematics

2 answers:

kotegsom [21]2 years ago

5 0

Let the original price be $ x

Now , Set up an equation and solve for x :

$\longrightarrow \tt \: 40 = x - 25\% \: of \: x$

$\longrightarrow \tt \: 40 = x - \frac{25}{100} x$

$\longrightarrow \tt40 = x - \frac{1}{4} x$

$\longrightarrow \tt \: 40 = \frac{4x - x}{4}$

$\longrightarrow \tt \: 160 = 3x$

$\longrightarrow \tt \: x = 53.33$

The original price is $ 53.33 .

------------------- HappY LearninG <3 ---------

lapo4ka [179]2 years ago

4 0

160 was the original price.
We know this because 25% is the same as I think of it as a quarter 25x4=100
So you would have to do 40x4=160
Your welcome.

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Its 40% because its just the fact ratio you know

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3 years ago

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Mkey [24]

Answer:

$X = \begin{bmatrix}1&3\\ 2&4\end{bmatrix}$

Step-by-step explanation:

The question we have at hand is, in other words,

$\begin{bmatrix}4&2\\ \:1&1\end{bmatrix}\left(X\right)=\begin{bmatrix}8&20\\ \:3&7\end{bmatrix}$ - where we have to solve for the value of $X$

If we have to isolate $X$ here, then we would have to take the inverse of the following matrix ...

$\begin{bmatrix}4&2\\ \:1&1\end{bmatrix}$ ... so that it should be as follows ... $\begin{bmatrix}4&2\\ \:1&1\end{bmatrix}^{-1}$

Therefore, we can conclude that the equation as to solve for " $X$ " will be the following,

$X=\begin{bmatrix}4&2\\ 1&1\end{bmatrix}^{-1}\begin{bmatrix}8&20\\ 3&7\end{bmatrix}$ - First find the 2 x 2 matrix inverse of the first portion,

$\begin{bmatrix}4&2\\ 1&1\end{bmatrix}^{-1}$ = $\frac{1}{\det \begin{pmatrix}4&2\\ 1&1\end{pmatrix}}\begin{pmatrix}1&-2\\ -1&4\end{pmatrix}$ = $\frac{1}{2}\begin{bmatrix}1&-2\\ -1&4\end{bmatrix}$ = $\begin{bmatrix}\frac{1}{2}&-1\\ -\frac{1}{2}&2\end{bmatrix}$

At this point we have to multiply the rows of the first matrix by the rows of the second matrix,

$X = \begin{bmatrix}\frac{1}{2}&-1\\ -\frac{1}{2}&2\end{bmatrix}\begin{bmatrix}8&20\\ 3&7\end{bmatrix}$ ,

$X = \begin{pmatrix}\frac{1}{2}\cdot \:8+\left(-1\right)\cdot \:3&\frac{1}{2}\cdot \:20+\left(-1\right)\cdot \:7\\ \left(-\frac{1}{2}\right)\cdot \:8+2\cdot \:3&\left(-\frac{1}{2}\right)\cdot \:20+2\cdot \:7\end{pmatrix}$ - Simplifying this, we should get ...