I tried posting this earlier but it didn't seem to work so I'm posting it again. (So sorry if this is a duplicate thread)
The word question is:
A test has 20 questions worth 100 points. The test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
I need to find the two equations and that's the part I don't understand. Could someone tell me what the equations are or explain what to do for me?
Other members have already laid out how to solve this specific example, but this is some advice on how to approach such questions in general:
The key to algebra in general is being able to either discuss different things in the same way, or to discuss the same things in different ways. In this case, we have two different viewpoints of the same things. With regards to the T/F questions and the MC questions, we know two things about them:
- We know that the total number of them is 20
- We know that the total number of their point values is 100
Now we need to name the values we don't know. That is to say, we need to assign our variables. Pick a name for the two things that don't already have letters or numbers.
We say, "Let T=the number of true/false questions"
And we say, "Let M=the number of multiple choice questions."
Think of those as the nouns in our sentences. Consider the first fact, that the number of them is 20. That means if you combine T and M, you get 20:
T + M = 20
For the next sentence, we're not talking about the number of the questions; we're talking about the number if their points. How many points do ALL of the true/False questions bring to the total? It is the number of the questions times the 3 points that each is worth, AKA "3T." And the total value of the multiple choice questions by the same logic, is "11M". Put them together and they add up to 100:
3T + 11M = 100
That is the type of thinking that you can use to set up the equations. If you think of it as literature, instead of math, and try to get the sentences to tell the correct story, it will simplify the process.
