An oak tree that is 220 years old produced acorns at two different rates. Until it reached maturity, it produced an average of 900 acorns a year. However, once the tree reached maturity, it produced an average of 2200 acorns a year. One particular tree, Angel Oak, has produced about 289,000 acorns in its lifetime. At what age did it reach maturity?

A.The tree reached maturity at 188 years.
B. The tree reached maturity at 138 years.
C.The tree reached maturity at 148 years.
D. The tree reached maturity at 150 years.

Question

An oak tree that is 220 years old produced acorns at two different rates. Until it reached maturity, it produced an average of 900 acorns a year. However, once the tree reached maturity, it produced an average of 2200 acorns a year.  One particular tree, Angel Oak, has produced about 289,000 acorns in its lifetime. At what age did it reach maturity?

A.The tree reached maturity at 188 years. 
B. The tree reached maturity at 138 years.
C.The tree reached maturity at 148 years.
D. The tree reached maturity at 150 years.

mathmale · Answer

"900 acorns per year" and "2200 acorns per year" are "rates of change.  
We don't know how many years it takes for the given tree to reach maturity, so we represent that number by x.  How many acorns would the tree have produced by the time it reaches maturity?  Remember, this is an algebra course, and so it's OK to express quantities algebraically if you don't have numeric values on hand.

anonymous · Answer

900 acorns per year x 220 years = 198,000 acorns by the time it matures?

anonymous · Answer

x = 198,000?

anonymous · Answer

Am I on the right track? What should I do next? @mathmale

mathmale · Answer

the oak tree ios now 220 years old.  That does not mean that the tree reached maturity after 220 years.  We don't know how many years it took the tree to reach maturity; that's why I represent "years to maturity" by x.

Care to try again?

How many acorns has the tree already produced when it reaches maturity?   Hint:  after x years, how many acorns will have been produced?

mathmale · Answer

Let x represent the # of years to maturity (which is less than 220).  You may have to invent a second variable.

1.  How many acorns has the tree produced by the time it reaches maturity?  How do you represent this?

2.  How many acorns does the tree produce between the year of maturity and its current age (220 years)?  What variable are you going to use to represent this number of years?

3.  You'll have one variable from #1, above, and one variable from #2, above.  Keeping in mind that both variables represent time (in years), write an expression for the sum of these two variables.

4.  Given that the total number of acorns produced over 220 years was 289,000, 
write an equation showing the sum of two terms that add up to 289,000.

5.  Solve this system of linear equations.

mathmale · Answer

I'd welcome questions if any of what I've typed above is unclear to you.

anonymous · Answer

I am unsure of how to write the linear equations...

anonymous · Answer

Okay I am going to try this... Let's see...

anonymous · Answer

How many acorns has the tree already produced when it reaches maturity?   Hint:  after x years, how many acorns will have been produced? 
I believe the answer to this is... the answer I got, right? 
198,000

anonymous · Answer

289,000 - 198,000 = 91,000

anonymous · Answer

Er... @mathmale Am I on the right track now? :D

mathmale · Answer

Mathias:  Let x:  number of years to maturity.  Let y=number of years of age after tree has reached maturity, up to 220 years.  What is the sum x+y?

The acorn production rate during the first x years is $$\frac{ 900 acorns }{ year }*x.$$

mathmale · Answer

Write a similar equation, involving y and the acorn production rate in effect AFTER maturity (after x years).

Add these two quantities together and equate this sum to 289,000.

I will not be on the 'Net much longer, but will be happy to continue this discussion tomorrow if you like.