This week we learned how to apply rational equations to real life scenarios.
In order to do this, there are some tips for reading and solving these word problems.
- Read problem and understand what is being asked
- Introduce a variable to represent an unknown number
- Write an equation using given info
- Solve
- Write answer in sentence. Check that the solution makes sense
What this means is that when presented with a word problem, it is good to read it a couple of times in order to completely understand and not miss anything. It would be a good idea to highlight any keywords like added, times, then, etc.
The variable is what is being asked for, it is the answer to the question. Using all that you know, you can then write an equation and solve it. Then answer in a sentence. If this sentence makes sense to the question asked, it should be the answer.
An example of using rational expressions to answer a question with proportions:
Koolaid is added to water to make a solution that is a drink. How much Koolaid must be added to 10L of water to make a solution that contains 70% Koolaid?
70% becomes ₇⁄10
₇⁄10 = x⁄10+x
because it says added to 10, it becomes x over 10 + x
Then we can cross multiply, so 7(10 + x) = 10x
70 + 7x = 10x
Then solve for x
70 = 3x
23.3 = x
23L Koolaid should be added to water in order for it to be 70% Koolaid