Question
Students graphed the growth rate over several weeks of two plants in their classroom. The equations of both plants are given where x represents the time in weeks and y represents the heights of the plants in inches.
Plant A: y = 1.8x + 3.1
Plant B: y = 2.3x + 1.9
Approximately how many weeks will it take for both plants to reach the same height? Round your answer to the nearest tenth.
1.9 weeks
2.4 weeks
3.1 weeks
7.4 weeks
Plant A: y = 1.8x + 3.1
Plant B: y = 2.3x + 1.9
Approximately how many weeks will it take for both plants to reach the same height? Round your answer to the nearest tenth.
1.9 weeks
2.4 weeks
3.1 weeks
7.4 weeks
Answers
GPT-4o mini
To find out when both plants reach the same height, we need to set the equations equal to each other:
For Plant A:
\[ y = 1.8x + 3.1 \]
For Plant B:
\[ y = 2.3x + 1.9 \]
Setting the two equations equal gives us:
\[ 1.8x + 3.1 = 2.3x + 1.9 \]
Now, let's solve for \( x \):
1. Subtract \( 1.8x \) from both sides:
\[ 3.1 = 2.3x - 1.8x + 1.9 \]
\[ 3.1 = 0.5x + 1.9 \]
2. Subtract 1.9 from both sides:
\[ 3.1 - 1.9 = 0.5x \]
\[ 1.2 = 0.5x \]
3. Finally, divide by 0.5:
\[ x = \frac{1.2}{0.5} \]
\[ x = 2.4 \]
Therefore, it will take approximately **2.4 weeks** for both plants to reach the same height.
The answer is **2.4 weeks**.
For Plant A:
\[ y = 1.8x + 3.1 \]
For Plant B:
\[ y = 2.3x + 1.9 \]
Setting the two equations equal gives us:
\[ 1.8x + 3.1 = 2.3x + 1.9 \]
Now, let's solve for \( x \):
1. Subtract \( 1.8x \) from both sides:
\[ 3.1 = 2.3x - 1.8x + 1.9 \]
\[ 3.1 = 0.5x + 1.9 \]
2. Subtract 1.9 from both sides:
\[ 3.1 - 1.9 = 0.5x \]
\[ 1.2 = 0.5x \]
3. Finally, divide by 0.5:
\[ x = \frac{1.2}{0.5} \]
\[ x = 2.4 \]
Therefore, it will take approximately **2.4 weeks** for both plants to reach the same height.
The answer is **2.4 weeks**.