A farmer owns a total of 32 ducks and lambs.The ducks and lambs have 110 legs altogether.How many lambs are there?
Question
A farmer owns a total of 32 ducks and lambs.The ducks and lambs have 110 legs altogether.How many lambs are there?
Solution
To solve this problem, we can use a system of linear equations.
Let's denote: D - the number of ducks L - the number of lambs
From the problem, we know two things:
- The farmer owns a total of 32 ducks and lambs. This can be written as: D + L = 32
- The ducks and lambs have 110 legs altogether. Since ducks have 2 legs and lambs have 4, this can be written as: 2D + 4L = 110
We can simplify the second equation by dividing everything by 2, which gives us: D + 2L = 55
Now we have a system of two equations:
D + L = 32 D + 2L = 55
Subtract the first equation from the second to get: L = 55 - 32 = 23
So, the farmer has 23 lambs.
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