I visited a beautiful flower garden yesterday and counted exactly 90 flowers. Each flower was either red or yellow, and the flowers were not all the same color. My friend made the following observation: No matter which two flowers you might have picked, at least one was bound to be red. From this observation, how many were red and how many were yellow?
I guessed on this one and I have the right answers on my online homework. But I don't know how to do it. Could someone help me so I actually know how to do it please?
thanks
To solve this problem, let's assume that there are "x" red flowers and "y" yellow flowers in the garden. We know that the total number of flowers is 90, so we can write the equation:
x + y = 90
Now, let's consider the observation made by your friend: No matter which two flowers you might have picked, at least one was bound to be red. This means that no matter what values x and y take, there should always be at least one red flower.
To understand this, let's consider the worst-case scenario where there are no red flowers in the garden. In that case, x would be 0, and all the flowers would be yellow. However, if we pick any two flowers from this garden, we wouldn't find any red flowers, contradicting your friend's observation. Thus, the assumption that there are no red flowers is incorrect.
This means that there must be at least one red flower in the garden. In other words, x cannot be 0. Therefore, the minimum value of x is 1.
Now, we can rewrite our equation as:
1 + y = 90
Subtracting 1 from both sides gives us:
y = 89
So, there is 1 red flower and 89 yellow flowers in the garden.
You can now use this approach to solve similar problems by following these steps:
1. Assign variables to the different quantities involved in the problem.
2. Formulate equations based on the given information.
3. Use logical reasoning or mathematical techniques to deduce additional information or constraints.
4. Solve the equations to find the values of the variables.