A botanist is monitoring the heights of two bamboo plants. Plant A is 20 inches tall and g… — ACT

A botanist is monitoring the heights of two bamboo plants. Plant A is $20$ inches tall and grows at a constant rate of $1.5$ inches per day. Plant B is $12$ inches tall and grows at a constant rate of $2.5$ inches per day. After how many days will Plant B be exactly $6$ inches taller than Plant A?

Answer: 14 days

Answer

The correct answer is 14 days.

The correct answer is

14

days because when we translate the relationship, we get the equation

12 + 2.5d = 20 + 1.5d + 6

. Solving this equation yields

d = 14

Step-by-Step Solution

Define the variable

d

as the number of days and write the expressions for the heights of both plants.

Plant A's height is

20 + 1.5d

inches, and Plant B's height is

12 + 2.5d

inches.

To represent the growth of each plant algebraically over time.

Set up an equation representing that Plant B's height is

6

inches more than Plant A's height.

12 + 2.5d = (20 + 1.5d) + 6

To translate the verbal relationship into a mathematical equation.

Simplify the equation and solve for

d

d = 14

To find the number of days that satisfies the given condition.

Key Concept

Translating and Solving Algebraic Word Problems

Estimated Time:1m 15s

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