The school store is running a promotion on school supplies. Different supplies are placed on two shelves. You can purchase 2 items from shelf A and 5 from shelf B for $20. Or you can purchase 5 items from shelf
A and 2 from shelf B for $29. This can be represented by the following system of equations,
{
2A + 5B = 20
5A + 2B = 29
Solve the system of equations by multiplying first.
The price is $. on shelf A and 5 on shelf B.
If the supplies on shelf A are normally $8 each and the supplies on shelf B are normally $3 each, how
much will you save on each package plan?
You save $ when buying the first package and $ for buying the second package.

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step-by-step explanation:

do have an equation or graph or

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