Farmer john has hens, geese, ducks, and two goats the number of hens equals the number if geese and ducks combined . There are 5 fewer geese than ducks. If the total number of animals is 40 how many are ducks
I need help!!!!!
I still need help!!!!!
that dose not help at all ._.
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To solve this problem, let's break it down step by step.
1. Let's assign some variables to the unknown quantities:
Let's say the number of hens is represented by "h",
the number of geese is represented by "g",
the number of ducks is represented by "d".
2. According to the problem, the number of hens equals the number of geese and ducks combined. So we can write this as an equation: h = g + d.
3. The problem also provides us with another piece of information: there are 5 fewer geese than ducks. This can be written as an equation: g = d - 5.
4. Now let's use the information that the total number of animals is 40: h + g + d + 2(goats) = 40.
5. Since we only care about the number of ducks, let's eliminate the other variables from the equation. Substituting the value of "g" from equation 3 into equation 2, we get: d - 5 = d - 5.
6. Simplifying equation 3, we get: h = 2d - 5.
7. Now let's substitute the value of "h" from equation 1, which gives us: g + d = 2d - 5.
8. Simplify equation 7, we get: g = d - 5.
9. Let's substitute the value of "g" from equation 8 into equation 7, which gives us: (d - 5) + d = 2d - 5.
10. Simplifying equation 9, we get: 2d - 5 = 2d - 5.
11. When we simplify this equation, we can see that the value of "d" does not affect the equation.
12. This means that the number of ducks can be any value since the equation will be true for any value of "d".
Therefore, from the given information, we can't determine the specific number of ducks.
Without the goats, total = 38.
H = G + D
D = G + 5
Substitute G+5 for D
H = G + G + 5 = 2G + 5
H + G + D = 38
Substitute G+5 for D and 2G+5 for H.
2G+5 + G + G+5 = 38
Combine terms to solve for G, then D.