The ratio of the number of goats in farm x to the number of goats in farm y was 9:4. After 35 goats were transferred from farm x to farm y,there was an equal number of goats in each farm. how many goats were there in each farm at first?
Set up equations to solve for
X=number of goats in farm x,
Y=number of goats in farm y.
"The ratio of the number of goats in farm x to the number of goats in farm y was 9:4." =>
X/Y=9/4 multiply by Y to get:
X=9Y/4.....................(1)
"After 35 goats were transferred from farm x to farm y,there was an equal number of goats in each farm." =>
X-35=Y+35.....................(2)
Substitute (1) in (2) and solve for Y, hence X.
To solve this problem, let's assign variables to the number of goats in each farm. Let's call the number of goats in farm x "x" and the number of goats in farm y "y".
According to the given information, the ratio of the number of goats in farm x to the number of goats in farm y was 9:4. This can be written as (x/y) = 9/4.
After 35 goats were transferred from farm x to farm y, the number of goats became equal in both farms. So, the new number of goats in farm x would be (x-35) and in farm y would be (y+35).
Now we can set up an equation based on the information given:
(x-35)/(y+35) = 1
Next, we can solve these equations to find the values of x and y.
Solving the first equation (x/y = 9/4) for x:
x = (9/4) * y
Substituting this value of x in the second equation:
((9/4) * y - 35) / (y + 35) = 1
Multiply both sides of the equation by y + 35 to get rid of the denominator:
9y - 35(y + 35) = y + 35
Distributing and simplifying:
9y - 35y - 1225 = y + 35
Combine like terms:
-26y - 1225 = y + 35
Add 26y to both sides:
-1225 = 27y + 35
Subtract 35 from both sides:
-1260 = 27y
Divide by 27:
y = -1260 / 27
y ≈ -46.66
Since we can't have a negative number of goats, we discard this solution.
Therefore, there is no valid solution for the number of goats in each farm given the initial information.