A math teacher drove by a playground that was full of boys and dogs.The teacher notice there were a total of 40 heads and 100 feet. Hom many boys and how many dogs were there?
b+d = 40
2b+4d = 100
solve as usual.
Hi
To solve this problem, we can use a system of equations.
Let's assume the number of boys is B and the number of dogs is D.
Since each person (boy or teacher) has one head, the total number of heads is given as 40:
B + D = 40
Since each boy has 2 feet and each dog has 4 feet, the total number of feet is given as 100:
2B + 4D = 100
Now, we have two equations:
B + D = 40 --(1)
2B + 4D = 100 --(2)
We can use the method of substitution to solve this system of equations.
From equation (1), we have B = 40 - D.
Now, substitute this expression for B in equation (2):
2(40 - D) + 4D = 100
Simplifying:
80 - 2D + 4D = 100
2D = 20
D = 10
Substitute the value of D back into equation (1) to find B:
B + 10 = 40
B = 30
So, there are 30 boys and 10 dogs in total.