There are 720 apple trees, peach trees and lemon trees altogether in an orchard. The number of apple trees is 2 times the number of lemon trees. The number of peach trees is half the number of apple trees. Find the number of each type of fruit trees in the orchard.
A = 2 L
P = A/2 so A = 2 P
so for starters P = L = A/2
P + A + L =720
A/2 + A + A/2 = 720
2 A = 720
A = 720/2
now go back and get P= L = 720/4
Let's represent the number of apple trees as A, the number of peach trees as P, and the number of lemon trees as L.
We are given that there are 720 trees in total, so we can write the equation:
A + P + L = 720 ----(1)
We are also given that the number of apple trees is 2 times the number of lemon trees, so we can write the equation:
A = 2L ----(2)
Finally, we are given that the number of peach trees is half the number of apple trees, so we can write the equation:
P = 0.5A ----(3)
Now we can substitute equations (2) and (3) into equation (1) to solve for the variables.
From equation (2), we can substitute 2L for A in equation (3):
P = 0.5(2L)
P = L
Now we substitute A, P, and L into equation (1):
A + P + L = 720
2L + L + L = 720
4L = 720
L = 720/4
L = 180
Now substitute L = 180 into equation (2) to find A:
A = 2L
A = 2(180)
A = 360
Finally, substitute L = 180 into equation (3) to find P:
P = 0.5A
P = 0.5(360)
P = 180
Therefore, there are 360 apple trees, 180 peach trees, and 180 lemon trees in the orchard.
To solve this problem, we can use algebraic equations to represent the given information. Let's assign variables to each type of tree:
Let A represent the number of apple trees.
Let P represent the number of peach trees.
Let L represent the number of lemon trees.
From the given information, we can create three equations:
Equation 1: A + P + L = 720 (The total number of trees in the orchard is 720.)
Equation 2: A = 2L (The number of apple trees is 2 times the number of lemon trees.)
Equation 3: P = (1/2)A (The number of peach trees is half the number of apple trees.)
Now, we can solve the system of equations to find the values of A, P, and L.
Let's substitute Equation 2 and Equation 3 into Equation 1:
2L + (1/2)A + L = 720
Combining like terms, we get:
(5/2)L + (1/2)A = 720
To simplify the equation further, we can multiply both sides by 2 to get rid of the fractions:
5L + A = 1440
Since Equation 2 states that A = 2L, we can substitute 2L in place of A:
5L + 2L = 1440
Combining like terms, we get:
7L = 1440
Now, divide both sides by 7 to solve for L:
L = 1440 / 7
Using a calculator, we find that L ≈ 205.71
Since we can't have a fraction of a tree, the number of lemon trees must be a whole number. Therefore, we can round 205.71 to the nearest whole number, which is 206.
Now that we have the value of L, we can substitute it back into Equation 2 to find A:
A = 2L
A = 2 * 206
A = 412
Finally, we can substitute the values of L and A into Equation 1 to find P:
A + P + L = 720
412 + P + 206 = 720
P = 720 - (412 + 206)
P = 720 - 618
P = 102
Therefore, the number of apple trees is 412, the number of peach trees is 102, and the number of lemon trees is 206.