Explain why receiving a 15% discount is the same as finding 85% percent of the original cost of an item. Then, explain how the mathematical properties and equivalent expressions helped them understand and solve the problem. Please answer!!

15% discount means you're paying 85% of the marked price because total is 100% and 100-15 = 85%

Let X be the naked price

Paid = marked price - discount

Paid = X - (15/100 × X)

Using distribution property,

Paid = X(1 - 15/100)

Paid = X[(100-15)/100]

Paid = X(85/100)

Which is 85/100 × X

Hence 85% of X

85% = 0.85

While 15% = 0.15

Step-by-step explanation:

Percentage is a fraction whose denominator is 100. So if we say 15%, we mean 15/100 = 0.15.

If want to find 15% of a 100, it means 15% of 100 = 15/100 × 100 = 15.

To find 85 % of 100 means 85/100 × 100= 85

hence subtraction of 15% from 100% is 85%

Therefore 15% = 15/100 = 0.15

While 85% is 85/100 = 0.85