If four times the brother's age is subtracted from three times the sister's age, the difference is 8. Give an equation that represents this statement using b as the age of the brother and s as the age of the sister.

Step-by-step explanation:

Let b is the age of the brother and s as the age of the sister.

It is given that if four times the brother's age is subtracted from three times the sister's age, the difference is 8.

We need to find an equation for the given statement.

Four times the brother's age = 4×b = 4b

Three times the sister's age = 3×s = 3s

Four times the brother's age is subtracted from three times the sister's age.

The difference is 8.

Therefore, the required equation is .

the monthly balance will be $75,000

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