Tree planted that was 2ft tall. It grew the same amount each month. After 2 years it was 5 ft tall. How tall was the plant after 8 months?

Question

benchmark question 

Answer 1

The tree grew 3' or 36" in two years    5 ft - 2 ft = 3 ft

Three feet divided by additional two years or 24 months

36" / 24 mo  =  1.5" each month

8 mo  *  1.5"  =  12" grew in 8 months

Originally the tree was 2 ft tall  so

2 ft  +  12"  =  3 ft

The tree was 3 ft tall after 8 months

 

Answer 2

Let's look at some information given:

When the tree was planted it was 2 ft tall.  From the rest of the information we see that this is the beginning.  

Next we see that the tree grew at a constant rate each month.  Thus, each month the tree grew a specific amount.  So, if we know how much it grew in a specific number of months, we can calculate the amount it grew in each month by division.

Next we see that the amount it grew in 2 years was the height at 2 years minus the height at 0 years (the beginning).  This is 5 ft minus 2 ft or a growth of 3 ft in 2 years.  Now we could calculate the growth per year, but the question asks about the height in 8 months.  Oops, better find the growth per month.  Since there are 12 months in a year, 2 years is 2x12=24 months.

Now dividing 3 ft growth by 24 months we find the growth per month is 1/8 foot.

So we can find the growth in 8 months by multiplying the growth each month by the number of months 8x1/8=1ft.

 

Since we started with a 2ft tree and in 8 months added 1ft the result is a tree 2+1=3ft tall.