a young Colorado spruce tree is growing at a rate of 20 cm per year. Currently, it is 244 cm tall. A 300 cm tall white spruce tree is growing at a rate of 12 m per year. In how many years will the two trees be the same height? Solve algebraically
300×12=hours
I'm sorry, but I do not understand your response. The problem is asking for the number of years it will take for the two trees to be the same height. Can you please provide the correct solution?
7 years
That is correct! Here is the algebraic solution:
Let x be the number of years it will take for the two trees to be the same height.
The Colorado spruce tree's height after x years is: 244 + 20x
The white spruce tree's height after x years is: 300 + 12x
We can set these two expressions equal to each other and solve for x:
244 + 20x = 300 + 12x
8x = 56
x = 7
Therefore, it will take 7 years for the two trees to be the same height.
To solve this algebraically, let's assume that "x" represents the number of years it takes for the two trees to be the same height.
For the young Colorado spruce tree, we know that its current height is 244 cm, and it is growing at a rate of 20 cm per year. So, the height of the Colorado spruce tree after "x" years would be: 244 + (20 * x).
For the white spruce tree, we know that its current height is 300 cm, and it is growing at a rate of 12 m per year. Since 1 m is equal to 100 cm, the rate can be converted to cm as follows: 12 m/year * 100 cm/m = 1200 cm/year. Therefore, the height of the white spruce tree after "x" years would be: 300 + (1200 * x).
Now we can set up an equation:
244 + (20 * x) = 300 + (1200 * x)
Let's solve for "x":
244 + 20x = 300 + 1200x
Combine like terms:
-976 = 1180x
Divide both sides by 1180:
-976 / 1180 = x
Simplify:
-0.827 = x
Therefore, it would take approximately 0.827 years for the two trees to be the same height algebraically.