FOR 14 POINTS Thalia, a quiz show contestant, answered 20 questions. She was awarded 2 points for every correct answer that she
2 answers:
Answer:
<em>The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.</em>
Step-by-step explanation:
Given
Total Questions = 20
Total Points = 28
Correct Answers = +2 points
Incorrect Answers = -1 point
Required
Spot the error in the viewer's calculation
The viewer represents the correct answers with x and the incorrect ones with y.
This implies that
Also, for every correct answers, she gets 2 points;
<em>This can be represented by 2x</em>
and for every incorrect answers, she gets -1 point
<em>This can be represented by -y</em>
This implies that
This is where the viewer made a mistake
The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;
Solving further
Add both equations together
Divide both sides by 3
Substitute in
Subtract 16 from both sides
<em>This implies that the contestant answered 16 questions correctly and 4 questions incorrectly</em>
<em></em>
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Answer:
ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.
Step-by-step explanation:
In order to solve the final ratio of lemon juice to water, let us start by determining the initial ratio of pure lemon juice to water in the first mix. This is done as follows:
Total volume of mixture = 60 liters
initial volume of water = 60 liters
initial volume of lemon juice = 0 liters
1) She removed 15 liters of the water and replaced it with 15 liters of pure lemon juice.
Volume of water = 60 - 15 = 45 liters
Volume of lemon juice = 15 liters
2) She removed 10 liters of the new mixture
Let us convert this amount removed into ratio:
New volumes of water and lemon juice after removing the 10 liters of mixture is calculated as follows:
3) and replaced it with 10 liters of water.
The final ratio of lemon juice to water:
Therefore, the final ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.