Question

Captain Salamander is crossing through a forest which is infested with some of his worst predators: Blue Jay birds and raccoons. He decides to count them carefully to decide if it worth the risk of continuing or whether it would be safer to head back home. He manages to count 16 heads and 42 legs. Can you help him work out how many birds and how many raccoons there were in the forest?

a) 10 birds, 6 raccoons
b) 6 birds, 10 raccoons
c) 8 birds, 8 raccoons
d) 12 birds, 4 raccoons

Answer 1

To solve the problem, set up a system of equations based on the given information. Solve the equations using the method of elimination or substitution. The final answer is 11 birds and 5 raccoons.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's represent the number of birds as 'b' and the number of raccoons as 'r'. From the given information, we know that the total number of heads is 16 and the total number of legs is 42. We can set up two equations based on this: The number of heads: b + r = 16. The number of legs: 2b + 4r = 42. We can now solve these equations using the method of substitution or elimination. Let's use the method of elimination: Multiply equation 1 by 2 to eliminate 'b': 2b + 2r = 32. Subtract equation 2 from equation 3 to eliminate 'b': 2b + 4r - (2b + 2r) = 42 - 32. Simplify and solve for 'r': 2r = 10. Divide both sides by 2 to find the value of 'r': r = 5. Now substitute the value of 'r' into equation 1 to find the value of 'b': b + 5 = 16. Subtract 5 from both sides to solve for 'b': b = 11. Therefore, there are 11 birds and 5 raccoons in the forest.