There are some frogs and some lily pads at a pond. If lily pads with frogs on them have two frogs each, then there are 3 lily pads with no frogs on it . If each lily pad has exactly one frog on it, then there are 3 frogs with no lily pad. How many frogs are at the pond?
halp :(
To find the number of frogs at the pond, let's consider the two scenarios separately:
Scenario 1: Lily pads with frogs on them have two frogs each.
Let's denote the number of lily pads with frogs as x. According to the information given, there are 3 lily pads with no frogs on them. So, the total number of lily pads would be x + 3.
As each lily pad has two frogs on it, the total number of frogs on the lily pads would be 2 * x.
Scenario 2: Each lily pad has exactly one frog on it.
In this case, the number of frogs and the number of lily pads would be the same. Let's denote this as y.
Now, we can set up two equations based on the scenarios:
Equation 1: x + 3 = y
This equation represents the total number of lily pads with no frogs in Scenario 1, which is equal to the total number of frogs with no lily pad in Scenario 2.
Equation 2: 2x = y
This equation represents the total number of frogs on the lily pads in Scenario 1, which is equal to the total number of frogs and lily pads in Scenario 2.
Now, we can solve these two equations simultaneously to find the values of x and y, which will give us the number of frogs at the pond.
By substituting the value of y from Equation 1 into Equation 2, we get:
2x = x + 3
Solving this equation:
2x - x = 3
x = 3
Substituting the value of x into Equation 1:
3 + 3 = y
y = 6
Therefore, in both scenarios combined, there are 3 frogs on the lily pads and 3 frogs without a lily pad, making a total of 6 frogs at the pond.