there are people walking their dogs at a park. There are 30 heads and 68 feet at the park. Write out the algebraic equations for this problem. Use P to stand for the number of people and D to stand for the number of dogs.
D + P = 30, therefore D = 30-P
4D + 2P = 68
Substitute 30-P for D in second equation and solve for P. Insert that value into the first equation and solve for D. Check by inserting both values into the second equation.
To solve this problem using algebraic equations, we need to define some variables and set up equations based on the given information.
Let's define:
P = the number of people walking their dogs
D = the number of dogs being walked
Based on the given information, we can set up two equations:
1. The number of heads equation:
Since each person and each dog has one head, the total number of heads would be equal to the sum of the number of people and the number of dogs.
So, the first equation is:
P + D = 30
2. The number of feet equation:
Each person has two feet, while each dog has four feet. So, the total number of feet would be equal to twice the number of people (2P) plus four times the number of dogs (4D).
Therefore, the second equation is:
2P + 4D = 68
Now, we have the following system of equations:
P + D = 30
2P + 4D = 68
These equations can be used to find the values of P and D, which represent the number of people and the number of dogs at the park, respectively.