Foxes and rabbits. The ratio of foxes to rabbits in the
Deerfield Forest Preserve is 2 to 9. If there are 35 fewer
foxes than rabbits, then how many of each are there?
let number of foxes be 2x
let number of rabbits be 9x
foxes = rabbits - 35
etc....
Thanks so much I can take it from there. I have problems converting a word problem to a math problem.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the number of foxes is "F" and the number of rabbits is "R".
According to the given information, the ratio of foxes to rabbits is 2 to 9. This can be written as:
F/R = 2/9
It is also stated that there are 35 fewer foxes than rabbits. We can express this relationship as:
F = R - 35
Now, we have a system of equations:
F/R = 2/9 ...(1)
F = R - 35 ...(2)
To solve for F and R, we can use substitution or elimination method. Let's choose the substitution method in this case.
We will solve equation (2) for F and substitute it into equation (1):
From equation (2), we have:
F = R - 35
Substituting this into equation (1), we get:
(R - 35)/R = 2/9
Now we can solve this equation for R:
9(R - 35) = 2R
9R - 315 = 2R
Rearranging the terms:
9R - 2R = 315
Simplifying:
7R = 315
Dividing both sides by 7:
R = 45
Now that we have the value of R (rabbits), we can substitute it back into equation (2) to find F (foxes):
F = R - 35 = 45 - 35 = 10
So, there are 10 foxes and 45 rabbits in the Deerfield Forest Preserve.