Jill planted two flowers in her garden. The first flower is 2 inches tall, and it is growing 2.25 inches each week. The second plant is 5.75 inches tall, and it is growing 1.5 inches each week. How many weeks will it be until the two plants are the same height?

Answer:it will take the two plants 6 weeks before the heights are the same

Step-by-step explanation:

Jill planted two flowers in her garden.

The first flower is 2 inches tall, and it is growing 2.25 inches each week. Since the growth rate is in an arithmetic progression, we will apply the formula for finding the nth term of the series

Tn = a + (n - 1) d

Tn = the nth height of the first flower

a = the initial height of the first flower

d = the common difference in height of the first flower weekly

n = number of weeks

From the information given,

For the first flower,

a = 2

d = 2.25

Tn?

n?

Tn = 2 + (n - 1) 2.25

For the second flower,

a = 5.75

d = 1.5

Tn?

n?

Tn = 5.75 + (n - 1) 1.5

To determine the number of weeks that it will take until the two plants are the same height, we would equate Tn for both flowers. It becomes

2 + (n - 1) 2.25 = 5.75 + (n - 1) 1.5

2 + 2.25n - 2.25 = 5.75 + 1.5n - 1.5

Collecting like terms

2.25n - 1.5n = 5.75 - 1.5 - 2 + 2.25

0.75n = 4.5

n = 4.5/0.75

n = 6 weeks