SOLUTION: Hi, this word probelm is really challenging me and I was wondering if you could help. The problem is "A test has twenty questions worth 100 points. The test consists of True/Fals

Question 95442: Hi, this word probelm is really challenging me and I was wondering if you could help. The problem is
"A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple-choice questions worth 11points each. How many multiple choice questions are on the test?"
Thanks sooo much!
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let T represent the number of True/False questions and let M represent the number of Multiple
Choice questions.
.
Since the total number of questions is 20 we know that the number of True/False questions
plus the number of Multiple Choice questions is equal to 20. In equation form this is:
.
T + M = 20 <=== remember this. It is equation 1.
.
Since True/False questions are worth 3 points, the number of points you could score on
these questions is T times 3 points or 3*T. And since the Multiple Choice questions
are worth 11 points each, the number of points you could score on these questions is M times
11 points or 11*M. Now if we add up the total number of points possible, the result is
100 points. In equation form this becomes:
.
3T + 11M = 100 <=== this is equation 2
.
Now let's return to equation 1 and subtract M from both sides. When we do this subtraction
the +M disappears from the left side and the equation becomes:
.
T = 20 - M
.
Then we can go to equation 2 and for T in that equation we can substitute 20 - M . This
substitution makes the second equation become:
.
3(20 - M) + 11M = 100
.
Do the distributed multiplication on the left side by multiplying 3 times each of the
terms in the parentheses to get:
.
60 - 3M + 11M = 100
.
Get rid of the 60 on the left side by subtracting 60 from both sides. This results in:
.
-3M + 11M = 40
.
Then combine the two terms on the left side by combining -3M and + 11M to get +8M and
this reduces the equation to:
.
8M = 40
.
Solve for M by dividing both sides of this equation by 8 ... the multiplier of M to get:
.
M = 40/8 = 5
.
This tells us that there are 5 Multiple Choice questions. So the remaining 15 questions
on the test must be True/False questions.
.
Check. If we got all 5 Multiple Choice questions correct we would score 11 points for
each of the five questions and this would give us 55 points. Then if we got all 15 True/False
questions correct at 3 points each, we would score 15 times 3 or 45 points. So the total
number of points on the test would be 55 + 45 = 100. This is the correct number of points
on the test so our answer is correct ... 5 Multiple Choice questions and 15 True/False
questions.
.
Hope this helps you to understand the problem and a way that you can solve it by writing two
equations from the information given in the problem.
.

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