Tom decides to pick up some pizzas and drinks for his family. He notices that the pizza costs the same as 7 drinks. The 2 pizzas and 8 drinks cost $33. What is the price of each item?

Drinks = $1.5

Pizza = $10.50

Step-by-step explanation:

let d = drinks

p = pizza

p = 7d  equation 1

2p + 8d = 33 equation 2

from equation 1, we know the price of one pizza, the price of two pizzas can be determined by multiplying by 2

2p = 7d x 2 = 14d  eqn 3

Substitute for 2p in equation 2  

14d + 8d = 33

22d = 33

Divide both sides of the equation by 22

d = $1.5

Substitute for d in equation 1

p = 1.5 x 7 = $10.5

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step-by-step explanation:

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