In an orchard, there were 84 durian and papaya trees. 1 2 of the durian trees is equal to 1 4 of the papaya trees. Find the difference in the number of durian and papaya trees in the orchard.
Let x be the number of durian trees.
The number of papaya trees is 84 - x
1/2 * x = 1/4 * (84 - x)
2x = 4(84 - x)
2x = 336 - 4x
6x = 336
x = <<56=56>>56
The number of durian trees is 56.
The number of papaya trees is 84 - 56 = <<84-56=28>>28.
There is a difference of 56 - 28 = <<56-28=28>>28 in the number of durian and papaya trees. Answer: \boxed{28}.
Let's represent the number of durian trees as "D" and the number of papaya trees as "P".
We are given that the total number of trees in the orchard is 84. So we can write the equation:
D + P = 84
We are also given that 1/2 of the durian trees is equal to 1/4 of the papaya trees. This can be written as:
1/2D = 1/4P
To make it easier to eliminate the fractions, we can multiply both sides of the equation by 4:
4 * (1/2D) = 4 * (1/4P)
2D = P
Now we have a system of equations:
D + P = 84
2D = P
We can solve this system of equations using substitution or elimination method.
Using substitution method:
From the second equation, we can solve for P:
P = 2D
Now we can substitute this expression for P in the first equation:
D + 2D = 84
3D = 84
D = 84/3
D = 28
Substituting this value of D back into the second equation:
P = 2 * 28
P = 56
So, there are 28 durian trees and 56 papaya trees.
The difference in the number of durian and papaya trees in the orchard is:
56 - 28 = 28
To find the difference in the number of durian and papaya trees in the orchard, we first need to determine the number of trees for each fruit.
Let's assume the number of durian trees is x, and the number of papaya trees is y.
We are given two pieces of information in the problem:
1) "1/2 of the durian trees is equal to 1/4 of the papaya trees." This can be written as:
(1/2)x = (1/4)y
2) "In an orchard, there were 84 durian and papaya trees." We know the total number of trees is 84, so we can write another equation:
x + y = 84
Now we have a system of two equations:
(1/2)x = (1/4)y
x + y = 84
To solve this system, we can use substitution or elimination method. Let's use substitution:
From the first equation, we can rewrite it to solve for x:
x = (2/1)*(1/4)y
x = (2/4)y
x = (1/2)y
Now we substitute this expression for x in the second equation:
(1/2)y + y = 84
Multiplying the first term by 2 to clear the fraction:
y + 2y = 168
Combining like terms:
3y = 168
Dividing both sides by 3:
y = 56
Now we substitute this value of y back into the second equation to solve for x:
x + 56 = 84
Subtracting 56 from both sides:
x = 28
Therefore, there are 28 durian trees and 56 papaya trees in the orchard.
To find the difference in the number of durian and papaya trees:
Difference = Number of durian trees - Number of papaya trees
Difference = 28 - 56
Difference = -28
So the difference in the number of durian and papaya trees in the orchard is -28. This means there are 28 more papaya trees than durian trees.