A dress costs p dollars. An 8% sales tax must be added to the cost of the dress. Martha wants to multiply the cost of the dress by 0.08 to find the tax and then add it to the cost of the dress. Esther thinks that the cost of the dress should be multiplied by 1.08. The expressions for the two methods are shown below.

Martha: p+0.08p

Esther: 1.08p

Are the two expressions equivalent? Explain.

What does this mean in terms of the methods outlined by Martha and Esther?

Yes, both expressions for the two method are equivalent.

Step-by-step explanation:

Let the cost of the dress be p as given.

Marta want to evaluate the tax which is proportional to the cost.

8% sales tax will correspond to (8/100) * p=0.08p

Then she will add 0.08 p to p to obtain 0.08p+p = p (0.08+1) = 1.08p

On the other hand, Esther thinks that the cost of the dress, p, should be multiplied by 1.08 to obtain 1.08p at once!

Thus both expressions are equivalent. Only that Martha is wanting to pay much attention to the details, while Esther is a quick one : -) !