1. In a farm, there were some hens and rabbits. Maria saw 140 legs. How many hens and rabbits did she see? Explain if you have more than one solution.
Answers
Chickens = 60 and rabbits = 52
The thing to do is make a couple of equations out of the given information, and use that model to solve. We know that 43 heads means there are 43 animals altogether. We also know from general knowledge that rabbits have four legs and chickens have 2. So:
Let R = total rabbit legs
Let C = total chicken legs
Equation 1: R/4 + C/2 = 43
Rabbit legs divided by 4 plus chicken legs divided by 2 = total heads.
The other piece of information we are given is that total legs = 112. This gives us another equation: R + C = 112. But for our model, we need to transform this equation a little, to get one of our variables isolated. This can be done by subtracting C from both sides. Doing that we get:
Equation 2: R = 112-C
This is the value of R in terms of C. We can now substitute this equivalent of R back into the original equation, getting it down to only one variable, C. Then we can go ahead and solve for C.
Substitute into equation 1:
112-C/4 + C/2 = 43
Set terms on left to common denominator:
112-C/4 + 2C/4 = 43
Combine terms on left:
112-C+2C/4 = 43
Multiply both sides by 4:
112-C+2C = 172
Subtract 112 from both sides:
-C+2C = 60
And combining terms on left gives the solution for C:
C = 60
Now substitute the value of C back into equation 2 of our model:
R = 112–60
And we get the solution for R:
R = 52
Recall that R and C = rabbit legs and chicken legs. So the last step is to substitute the values for them that we have found back into equation 1:
52/4 + 60/2 = 43
Do the divisions:
13 + 30 = 43
The numbers add to 43, so we know our work is correct. The farm has 13 rabbits and 30 chickens.
Step-by-step explanation:
IzzfzlzyrruPyszez63/*4***of 4*of 330*03*of*30*64*64*3*of*of 3*3*of 0*of*6*46*46*4*//*4*