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 for height

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

Step2: Set heights equal

$3 + t = 4 + 0.5t$

Step3: Solve for $t$

Subtract $0.5t$ from both sides: $3 + 0.5t = 4$
Subtract 3 from both sides: $0.5t = 1$
Multiply by 2: $t = 2$

Step1: Define variables for cost

Let $x$ = number of classes, $C_m$ = member cost, $C_n$ = non-member cost.
$C_m = 20 + 3x$
$C_n = 5x$

Step2: Set costs equal

$20 + 3x = 5x$

Step3: Solve for $x$

Subtract $3x$ from both sides: $20 = 2x$
Divide by 2: $x = 10$

Answer:

2 years

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Problem 21