Question

1. plants a plant nursery is growing a tree that is 3 ft tall and grows at an average rate of 1 ft per year. another tree at the nursery is 4 ft tall and grows at an average rate of 0.5 ft per year. after how many years will the trees be the same height?
2. fitness at a local fitness center, members pay a $20 membership fee and $3 for each aerobics class. nonmembers pay $5 for each aerobics class. for what number of aerobics classes will the cost for members and nonmembers be the same?

Explanation:

Problem 20

Step1: Define variables and equations

Let $t$ = number of years.
Height of first tree: $h_1 = 3 + 1t$
Height of second tree: $h_2 = 4 + 0.5t$

Step2: Set heights equal

$3 + t = 4 + 0.5t$

Step3: Solve for t

Subtract $0.5t$ and 3:
$t - 0.5t = 4 - 3$
$0.5t = 1$
$t = \frac{1}{0.5} = 2$

Step1: Define variables and equations

Let $x$ = number of classes.
Cost for members: $C_m = 20 + 3x$
Cost for nonmembers: $C_n = 5x$

Step2: Set costs equal

$20 + 3x = 5x$

Step3: Solve for x

Subtract $3x$:
$20 = 5x - 3x$
$20 = 2x$
$x = \frac{20}{2} = 10$

Answer:

2 years

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Problem 21