Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Question

On the windowsill is a plant that is 14 centimeters tall. It is growing 10 centimeters per week. A second plant, which is 49 centimeters tall, is on the coffee table. It is growing 3 centimeters per week. Eventually the two plants will be the same height. How many weeks will that take? How tall will the plants be?

In
weeks, each plant will be
centimeters tall.

Answer 1

Let \( t \) be the number of weeks.

The height of the first plant (on the windowsill) can be expressed as: \[ h_1 = 14 + 10t \]

The height of the second plant (on the coffee table) can be expressed as: \[ h_2 = 49 + 3t \]

We want to find when the heights of both plants are equal: \[ 14 + 10t = 49 + 3t \]

Now, we will solve this equation.

1. Subtract \( 3t \) from both sides: \[ 14 + 10t - 3t = 49 \] \[ 14 + 7t = 49 \]

2. Subtract 14 from both sides: \[ 7t = 49 - 14 \] \[ 7t = 35 \]

3. Divide by 7: \[ t = 5 \]

Now we substitute \( t = 5 \) back into the equations for the heights of the plants.

For the first plant: \[ h_1 = 14 + 10(5) = 14 + 50 = 64 \text{ centimeters} \]

For the second plant: \[ h_2 = 49 + 3(5) = 49 + 15 = 64 \text{ centimeters} \]

Thus, in \( \boxed{5} \) weeks, each plant will be \( \boxed{64} \) centimeters tall.