SOLUTION: On a History Exam, each multiple-choice question is worth 3 points,and each true false question is worth 2 points. Vanessa answered 28 questions correctly on the exam and earned a

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Question 101174This question is from textbook Elementary and Intermediate Algebra
: On a History Exam, each multiple-choice question is worth 3 points,and each true false question is worth 2 points. Vanessa answered 28 questions correctly on the exam and earned a score of 77 points.How many multiple-choice questions did she answer correctly and how many true-false questions did she answer corectly? This question is from textbook Elementary and Intermediate Algebra

Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
First lets set some variables.
Let: x = multiple choice questions answered correctly
Let: y = true false questions answered correctly
Now the problem tells us that:
multiple choice questions are worth 3 points
true false questions are worth 2 points
Vanessa answered 28 questions correctly
Vanessa earned a score of 77
Ok so lets put all this information into a system of equations
x + y = 28
Thats the number of multiple choice questions plus the number of true false questions equals the number of questions correctly answered which is 28
Next we can say:
3x + 2y = 77
This is 3 times the number of multiple choice questions plus 3 times the number of true false questions equals the score vanessa made on the test which is 77

Now that we have a system of equations we can solve for x and y.
x + y = 28
3x + 2y = 77
To solve these system of equations I will use the substitution method.
Take the first equations and set it equal to x
x + y = 28
x = 28 - y
now substitute this value for x into the second equation and solve for y
3x + 2y = 77
3(28 - y) + 2y = 77
84 - 3y + 2y = 77
-y = -7
y = 7
So vansessa answered 7 true false questions correctly
now take the first equation and substitute 7 for y and solve for x
x + y = 28
x + 7 = 28
x = 21
So Vanessa answered 21 multiple choice questions correctly
Check answers in both equations
x + y = 28
21 + 7 = 28
28 = 28
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3x + 2y = 77
3(21) + 2(7) = 77
63 + 14 = 77
77 = 77