math question !!!

Question

Logan genetically engineered a new type of fir tree and a new type of pine tree. The combined height of one fir tree and one pine tree is 21 meters. Additionally, if Logan stacked 4 of his fir trees on top of each other, they would be 24 meters taller than one of his pine trees.

Answer 1

The problem here is that the question has been left out entirely : )  My guess is that it isn't, "So, how many inches of rain fell in Baltimore?"  Maybe it's along the lines of, "How tall is each type of tree (in meters)?"

 

And that is our first clue to solving this problem.  In any word problem, one of the first steps is assigning variables to unknown quantities which you need a concrete number for in order to achieve a solution. And most questions automatically indicate the presence of an unknown quantity, so defining variables according to the question itself is usually a great starting place. 

 

So let's do exactly that.  The question asks how tall each tree is (unknowns).  So we'll define our variables as the height of each type of tree:

 

x = height of a fir tree (in meters)

y = height of a pine tree (in meters)

 

Many word problems make stupid assumptions, and this one is no exception.  In real life, all trees of one type are NOT the same height.  But in Ljisdjfs's Word Problem Land, we have to assume that they are.  This is obviously not the world we live in, so let's pack our suitcases for a brief journey to the heart of stupid, where we may find an answer to the question.

 

Our journey begins by translating English into math:

 

Equation 1:

"One fir tree"

x

 

"One pine tree"

y

 

"The combined height of one fir tree and one pine tree"

x + y

 

"is 21 meters"

= 21

 

All together now:

"The combined height of one fir tree and one pine tree" "is 21 meters"

                          x + y                                                                 = 21

x+y=21.  Done.

 

Equation 2: Developing this one isn't quite as straightforward, but we'll build the pieces, and then put them together.

 

The length of 4 fir trees stacked on top of the other:

x + x + x + x

=4x

 

"would be"

=

 

"one of his pine trees"

y

 

"24 meters taller than" "one of his pine trees"

               24    +               y

 

"if Logan stacked 4 of his fir trees..." "they would be" "24 meters taller than" "one of his pine trees"

                    4x                                                   =                             24       +                       y

 

4x = y + 24.  Done.

 

So, we have two equations:

x+y=21

4x = y + 24

 

Let's rearrange the second equation so all variables are on the left, and rewrite the group of equations again:

 

x  + y = 21

4x - y = 24

 

If we add both equations, y cancels:

x + 4x + y - y = 21 + 24, or

5x = 45.  divide both sides by 5:

x = 9

 

substitute this value of x into the first equation to find y:

 

9 + y = 21.  Subtract 9 from both sides:

y = 12.

 

A fir tree is 9 meters tall, and a pine tree is 12 meters tall.

 

 

 

Answer 2

You would need 2 unknowns for this problem since there are 2 types of trees.  

 

Let f = height of fir a tree and p = height of a pine tree.

 

Now translate the words.  

 

The combined height of one fir and one pine tree is 21 meters.  The equation would be f + p = 21

 

Four fir trees would be 24 meters taller than one pine tree.  The equation would be 4f = 24 + p

 

You have a system of equations.  One way to solve this system would be to solve the first equation for p.  This would 

 

give you p = 21 - f.

 

Take the 21 - f and substitute it into the 2nd equation for p.

 

This will give you 4f = 24 + 21 - f.

 

Solving this equation, you would add f to both sides and combine 24 +21 giving you 5f = 45.

 

Divide both sides by 5 and you get f = 9 meters.  Thus the height of the fir tree is 9 meters.  

 

To find the height of the pine tree put the 9 meters back into the first equation (f + p =21) and you have

 

9 + p = 21.  When you solve this equation you would find that p = 12 meters.

 

CHECK:  Put the 9 meters for the fir tree and 12 meters for the pine back into BOTH equations and see if BOTH are 

 

correct.

 

f + p = 21     9 + 12 = 21   is correct

 

4f = 24 + p  4(9) = 24 + 12

                    36 =   36   is also correct

 

The check works.  So a fir tree is 9 meters tall and a pine tree is 12 meters tall.

 

I don't know what the question was, but this might help.