Question

Morgan bought a pair of shoes at a sale of 25%. If the amount she paid was $1000, find the marked price.

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Answer 1

$\large\bold{\underline{\underline{Solution:-}}}$

$\underline{\bf{Given\::-}}$

Discount on a pair of shoes, (D) = 25%

Cost price of shoes, (C.P) = Rs.1000

$\underline{\bf{Explanation\::-}}$

Using formula of the marked price, (M.P) when given C.P;

$\boxed{\bf{C.P = M.P\bigg(\frac{100-Discount}{100} \bigg)}}$

A/q

$\mapsto\tt{cost\:price = Marked\:price \bigg(\dfrac{100 - Discount }{100} \bigg)}$

$\mapsto\tt{1000 = Marked\:price \bigg(\dfrac{100 - 25}{100} \bigg)}$

$\mapsto\tt{1000 = Marked\:price \bigg(\dfrac{75}{100} \bigg)}$

$\mapsto\tt{1000 =\dfrac{75\:Marked\:price}{100}}$

$\mapsto\tt{1000\times 100 = 75\:Marked\:price}$

$\mapsto\tt{100000 = 75\:Marked\:price}$

$\mapsto\tt{Marked\:price = \cancel{\dfrac{100000}{75} }}$

$\mapsto\bf{Marked\:price = Rs.1333.3}$

Thus,

The Marked price of a pair of shoes will be Rs.1333.3

Answer 2

$\large{\boxed{\boxed{\sf Let's \: Underst \: and \: Concept!}}}$

Here, we have given that Morgan bought a pair of shoes from a sale at a discount of 25%. She paid a amount of $1000. What will be the marked price. So, here f1st we let Marked Price as 'x'. We, know that Discount is M.P. - Amount. Now, Discount% is Discount divided marked price multiply 100. By this we will find the value of x which is marked price.

$\pink{\underline{\textsf{Note:}}}$ Here, I let the value of Marked Price as 'x' but u can let what you wish.

$\huge{\underline{\boxed{\sf AnSwer}}}$

____________________________

$\large{\underline{\textbf{Given:-}}}$

• Sale = 25%
• Amount Paid = $1000

$\large{\underline{\textbf{Find:-}}}$

• Marked Price

$\large{\underline{\textbf{Solution:-}}}$

Let, Marked Price be $'x'

Now,

$\underline{\boxed{\sf Discount = Marked \: Price - Amount}}$

$\sf where \small{\begin{cases} \sf Marked \: Price = \ x \\\sf Amount =\ 1000 \end{cases}}$

$\bigstar\textsf{Substituting these values:-}$

$:\implies\sf Discount = Marked \: Price - Amount$

$:\implies\sf Discount = x - 1000$

Now,

$\underline{\boxed{\sf Discount\% = \dfrac{Discount}{Marked \: Price} \times 100}}$

$\sf where \small{\begin{cases} \sf Marked \: Price = \ x \\\sf Discount\% =25\% \\ \sf Discount = x - 1000 \end{cases}}$

$\bigstar\textsf{Substituting these values:-}$

$\dashrightarrow\sf Discount\% = \dfrac{Discount}{Marked \: Price} \times 100$

$\dashrightarrow\sf 25 = \dfrac{x - 1000}{x} \times 100$

$\dashrightarrow\sf 25 = \dfrac{100(x - 1000)}{x}$

$\bigstar\textsf{Cross-multiplication:-}$

$\dashrightarrow\sf 25 \times x= 100(x - 1000) \times 1$

$\dashrightarrow\sf 25x= 100(x - 1000)$

$\dashrightarrow\sf 25x= 100x - 100000$

$\dashrightarrow\sf 25x - 100x = - 100000$

$\dashrightarrow\sf -75x = - 100000$

$\dashrightarrow\sf \not-75x = \not- 100000$

$\dashrightarrow\sf 75x = 100000$

$\dashrightarrow\sf x = \dfrac{100000}{75}$

$\dashrightarrow\sf x = \ 1333.333(approx.)$

$\dashrightarrow\sf x = \ 1333.3$

$\underline{\boxed{\sf\therefore Marked\:Price\:of\:shoes\:is\:\ 1333.3}}$