Angel is going to a carnival that has games and rides. Each game costs $1.75 and each ride costs $5. How much would Angel have to pay if he wanted to play 9 games and go on 4 rides? How much would Angel have to pay if he wanted to play gg games and go on rr rides?

Total cost= $35.75

Step-by-step explanation:

Giving the following information:

Each game costs $1.75 and each ride costs $5.

First, we will structure the total cost formula:

Total cost= 1.75x + 5y

x= number of games

y= number of rides

Now, the total cost of 9 games and 4 rides:

Total cost= 1.75*9 + 5*4

Total cost= $35.75

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