The value of \( t = 7.5 \) in your problem indicates the time in months when both Plant A and Plant B will reach the same height.
To clarify further:
- The expression for Plant A's height after \( t \) months is given by \( 25 + 10t \).
- The expression for Plant B's height after \( t \) months is given by \( 10 + 12t \).
By setting these two equations equal to each other (since you're looking for the time when both plants are the same height), you found that:
\[ 25 + 10t = 10 + 12t \]
Solving this leads to \( t = 7.5 \).
What this means:
- After 7.5 months, both Plant A and Plant B will be exactly the same height.
- To find the actual height at that time, you can substitute \( t = 7.5 \) into either height equation:
For Plant A: \[ \text{Height of A} = 25 + 10(7.5) = 25 + 75 = 100 \text{ cm} \]
For Plant B: \[ \text{Height of B} = 10 + 12(7.5) = 10 + 90 = 100 \text{ cm} \]
Both plants will be 100 cm tall after 7.5 months.
Thus, it is not 7.5 cm tall at the same time; rather, the plants will be the same height of 100 cm after 7.5 months.
1 answer