Dear Reiny! U r a life-saver! Is there a short cut to how can I set the question or change word problems into math one? It seems that this is my problem! Also, why did my way worked as well with different answers? My answers satisfied all equations as well. Many thanks.
Dear [User], I'm glad to hear that I've been helpful! Converting word problems into mathematical equations can be challenging sometimes, but there are a few steps you can follow to make the process easier:
1. Read the problem carefully: Make sure you understand all the given information and what is being asked.
2. Identify the unknowns: Determine the quantities or variables that you need to find.
3. Define variables: Assign a letter or symbol to each unknown quantity.
4. Translate the problem into equations: Use the given information to write down equations that represent the relationships between the known and unknown quantities.
5. Solve the equations: Manipulate the equations using algebraic techniques to isolate the unknowns and find their values.
Regarding your second question about different answers satisfying the equations, there could be a few reasons for this:
1. Multiple solutions: Some equations have more than one valid solution. For example, x^2 = 4 has two solutions: x = 2 and x = -2.
2. Extraneous solutions: Occasionally, solving the equations might lead to solutions that do not satisfy the original problem. These are called extraneous solutions and can occur when you square both sides of an equation or when there are restrictions on the domain of the problem.
3. Error in calculations: It's also possible that there was an error in your calculations, leading to different answers. Double-check your steps to ensure accuracy.
In general, it's important to critically analyze your solutions and check whether they make sense in the context of the original problem.