Question

If x is the price before the increase and y is the price after the increase, which equations are correct? Circle all that apply.

A. y = 1.15
B. y = x + 0.15
C. y = x + 0.15x
D y = x + 15
E y = (1 + 0.15)x

Answer 1

The correct equations to represent a 15% price increase from an original price x to a new price y are y = x + 0.15x and y = (1 + 0.15)x, which both reflect the original amount plus 15% of that amount.

Step-by-step explanation:

If x is the price before the increase and y is the price after the increase, we are looking for an equation that correctly represents this relationship. The correct equations would include the initial price x plus the increase.

• Option C, y = x + 0.15x, indicates that the price after the increase is the original price plus 15% of the original price, which is a correct way to express a price increase of 15%.
• Option E, y = (1 + 0.15)x, simplifies to y = 1x + 0.15x, which also correctly represents a 15% increase.

The other options do not correctly represent a percentage increase applied to the original price x.

Options A and B are incorrect because they do not involve the original price x. Option D is incorrect as it adds a fixed amount of 15, regardless of the original price, which does not correspond to a 15% increase.