Question

Lucia and Maria are business women who decided to invest money by buying farm land in Brazil. They started their investments at the same time, and each month they buy more land. Lucia bought 111111 hectares of land in the first month, and each month afterwards she buys 555 additional hectares. Maria bought 666 hectares of land in the first month, and each month afterward her total number of hectares increases by a factor of 1.41.41, point, 4. In which month will Maria's amount of land first exceed Lucia's amount of land?

Answer 1

In 7th month Maria's amount of land first exceed Lucia's amount of land.

Explanation:

Lucia and Maria started their investment by buying farm land in Brazil at the same time.

According to the question it is given that

Lucia bought land in the first month = 11 hectares

afterwards she buys additional land each month = 5 hectares

Maria buys in the first month = 6 hectares

afterwards she buys additional land each month = factor of 1.4

Here is a table, that shows the Maria's and Lucia's amount of land in each month.

Months Lucia's land 11+(5) Maria's land 6(1.4)

(in hectare) (in hectare)

1 11 6

2 16 8.4

3 21 11.76

4 26 16.46

5 31 23

6 36 32.2

7 41 45.08

So from the above data we can see in 7th month Maria's amount of land would exceed Lucia's amount of land.

Answer 2

In 7th month.

Explanation:

Let the number of months = x.

It is given that Lucia bought 11 hectares of land in the 1st month and added 5 hectares each month after.

Amount of land Lucia bought,
`L(x)=11+5(x-1)`

Now, Maria bought 6 hectares of land in the 1st month and increases land by a factor of 1.4 each month after.

Amount of land Maria bought,
`M(x)=6(1.4)^(x-1)`

So, we will form the table for the values of the functions representing the lands,

Months (x) Lucia,
`L(x)=11+5(x-1)` Maria,
`M(x)=6(1.4)^(x-1)`

1 11 6

2 16 8.4

3 21 11.8

4 26 16.5

5 31 23

6 36 32.2

7 41 45.1

8 46 63.1

So, we see that,

In 7th month, Maria'a amount of land will exceed Lucia's amount of land.