50 birds were resting on two trees. 5 birds from the first tree flew away. Another 15 birds from else where flew to the second tree. The number of birds on the second tree was 3 times as many as the number of birds on the first one. How many birds were on each tree at first?
to start,
x+y = 50
after the migrations,
y+15 = 3(x-5)
Now just solve for x and y
x=32 y=18
Let's denote the initial number of birds on the first tree as x and the initial number of birds on the second tree as y.
According to the given information, we know that the total number of birds on both trees is 50.
Therefore, we can write the equation:
x + y = 50 (Equation 1)
We also know that 5 birds from the first tree flew away, so the new number of birds on the first tree is (x - 5).
Similarly, 15 birds from elsewhere flew to the second tree, so the new number of birds on the second tree is (y + 15).
According to the given information, the number of birds on the second tree is 3 times the number of birds on the first tree.
Therefore, we can write the equation:
y + 15 = 3(x - 5) (Equation 2)
Now, we can solve this system of equations to find the values of x and y, which represent the initial number of birds on each tree.
Substituting equation 1 into equation 2, we get:
y + 15 = 3(50 - y)
Expanding the equation and simplifying, we have:
y + 15 = 150 - 3y
4y + 15 = 150
4y = 135
y = 135 / 4
y = 33.75
Since we cannot have a fraction of a bird, we can round y to the nearest whole number, which is 34.
Substituting the value of y into equation 1, we get:
x + 34 = 50
x = 50 - 34
x = 16
Therefore, the initial number of birds on the first tree was 16, and the initial number of birds on the second tree was 34.
Let's represent the number of birds on the first tree as 'x' and the number of birds on the second tree as 'y'.
According to the given information, there were initially 50 birds resting on both trees combined. So we can write the equation:
x + y = 50 ........(Equation 1)
Next, it is mentioned that 5 birds from the first tree flew away. So the new number of birds on the first tree will be (x-5).
Also, 15 birds from elsewhere flew to the second tree. So the new number of birds on the second tree will be (y+15).
It is given that the number of birds on the second tree is 3 times as many as the number of birds on the first tree. Mathematically, we can express this as:
(y+15) = 3(x-5)
y + 15 = 3x - 15
3x - y = 30 ........(Equation 2)
Now we have two equations, Equation 1 and Equation 2, with two variables (x and y). We can solve these equations simultaneously to find the values of x and y, which represent the number of birds on the first and second trees, respectively.