Create your own word problem that uses a system of equations to solve. Your problem must include the following words: beach,hammock,dance,and troll.
Sure! Here's a word problem that involves a system of equations:
At the beach, there is a group of friends who want to relax in hammocks and also have a dance party. Are they able to do both while avoiding a troll? Let's find out!
Let's represent the number of hammocks as 'h' and the number of friends who want to dance as 'd'. We know that each person needs their own hammock, so the number of friends is the same as the number of hammocks.
Now, let's introduce the troll. The troll wants to join the dance party, but only if the number of hammocks is not equal to the number of friends. We can represent the presence of the troll with a variable 't'.
Based on the conditions above, we can set up a system of equations:
Equation 1: h = d (Each person needs their own hammock)
Equation 2: h ≠ d (The troll joins the dance party if the number of hammocks is not equal to the number of friends)
To solve this system, we can substitute Equation 1 into Equation 2:
d ≠ d
As we can see, this equation is not possible. It means that the troll cannot join the dance party while ensuring each friend has their own hammock. Therefore, the friends can have both a relaxing time in the hammocks and a dance party without any interference from the troll if the number of hammocks and friends is the same.