A department store gives away a $10 gift card to every 20th customer and a $15 gift card to every 45th customer. a. Which customer will be the first to receive bbth gift cards? Customer
b. After this customer receives both gift cards, what is the total amount in gift cards that the store has given away?

The LCM(20, 45) = 180. So, it will be the 180th customer who will receive both gift cards. 180 / 20 = 9 - $10 gift cards were given away.

Step-by-step explanation:

14

step-by-step explanation:

14 x 3 = 42

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