What does your answer of 7.5 mean in this problem?

Plant A's height after t months: 25+10t
Plant B's height after t months: 10+12t
25 + 10t = 10 + 12t
t = 7.5

Plant A and Plant B will be the same height after 7.5 months.

Plant A and Plant B will be 7.5 cm tall at the same time.

1 answer

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:

  1. After 7.5 months, both Plant A and Plant B will be exactly the same height.
  2. 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.