Astore marks up all of their merchandise by 70%. the floor price of a scarf is $117.25.
1. what was the stores purchase price before the markup for this item?

  $68.97

Step-by-step explanation:

Markup is the difference between the cost of an item and the price at which it is sold:

  cost price + markup = selling price

Here, the markup is said to be 70%. The base for that percentage can be either the cost price or the selling price. The way this question is worded suggests the markup is 70% of the cost price.

So, we have ...

  cost price + 0.70 × cost price = selling price

or

  cost price × (1 + 0.70) = selling price

__

Then, to find the cost price, we can divide by its coefficient in this equation. Doing that gives ...

  cost price = (selling price)/1.70

  cost price = $117.25/1.70 = $68.97

The store's purchase price before the markup for this item was $68.97.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt