Luke has 4 more than triples the number of model cars that Andrew has. Luke has 31 cars. How many cars does Andrew have? {Write and solve an equation}

Andrew has 9 cars

Step-by-step explanation:

Let's start by defining what our unknowns are and how to name them:

For the number of cars Andrew has: let's use the letter A

For the number of cars Luke has: let's use the letter L

Not write the first sentence in mathematical terms:

"Luke has 4 more than triples the number of cars that Andrew has."

L = 3 * A + 4

The second phrase results on a very simple equation since it just states the number of cars that Luke has:

L = 31

Now we can combine these two equations by replacing the variable "L" in the first equation with the second equation and then solve for A:

L = 3 * A + 4

31 = 3 * A +4

31 - 4 = 3 * A

27 = 3 * A

A = 27/3

A = 9

Therefore, Andrew has 9 cars.

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