Question

A $60\$$ jacket is on sale for 20% off. How much is the jacket after the discount?

Answer 1

Hint: We first find the formula to form the discounted or hiked price over a certain price. Using the formula and putting the required values for our given problem, we find the required solution of the problem.

Complete step by step solution:
A $60\$$ jacket is on sale for 20% off. We need to find the price of the jacket after the discount.
Let us assume the price of any particular thing as $x$. We have y% discount on the price. Then the final price after the discount becomes $x\left( 1-\dfrac{y}{100} \right)$.
In case of price hike, we will use the binary operation of addition instead of subtraction. The formula changes to $x\left( 1+\dfrac{y}{100} \right)$.
For our given problem we place the values where $x=60,y=20$.
The discounted price will be $60\left( 1-\dfrac{20}{100} \right)$.
We first complete the division of $\dfrac{20}{100}$.
For our given fraction $\dfrac{20}{100}$, the G.C.D of the denominator and the numerator is 20.
Now we divide both the denominator and the numerator with 20 and get $\dfrac{{}^{20}/{}_{20}}{{}^{100}/{}_{20}}=\dfrac{1}{5}$.
Putting the value, we get $60\left( 1-\dfrac{20}{100} \right)=60\left( 1-\dfrac{1}{5} \right)=\dfrac{60\times 4}{5}$.
The multiplication gives $60\times 4=240$.
The division gives $\dfrac{240}{5}=48$.

Therefore, the discounted price of the jacket will $48\$$

Note: We also could use the concept of 100. We use the main price as 100. We adjust the price hike or discount on 10. For our problem the discount was 20% which gives the discounted price as $100-20=80$. This 100 is equal to $60\$$ in the real case and we need to find the 80.
So, the discounted price is $60\times \dfrac{80}{100}=48$.