There were 20 questions in a quiz. For each question answered correctly, 6 points were awarded. For each question answered incorrectly, 4 points were deducted. For each question left blank, no points were awarded or deducted.
(a) Bernard answered all the questions in the quiz but obtained a score of zero. How
many questions did Bernard answer correctly?
(b) Raymond scored 16 for the quiz. The number of questions he answered correctly is the same as the questions he answered incorrectly. How many questions did he leave blank?
Let's assume that Bernard answered x questions correctly.
He also answered (20 - x) questions incorrectly.
According to the given information, the total score he obtained is 0, so we can write the equation:
6x - 4(20 - x) = 0
6x - 80 + 4x = 0
10x - 80 = 0
10x = 80
x = 8
Therefore, Bernard answered 8 questions correctly.
Let's assume that Raymond answered x questions correctly.
According to the given information, he also answered x questions incorrectly.
The total score he obtained is 16, so we can write the equation:
6x - 4x = 16
2x = 16
x = 8
Therefore, Raymond answered 8 questions correctly.
Since the number of questions he answered correctly is the same as the questions he answered incorrectly, he answered a total of:
8 + 8 = 16 questions
There were 20 questions in total, so he left:
20 - 16 = 4 questions blank. Answer: \boxed{4}.
To solve these problems, we'll use a system of equations. Let's denote:
C = number of questions answered correctly
I = number of questions answered incorrectly
B = number of questions left blank
(a) We know that Bernard's score is zero. From the information given, we can set up the equation:
6C - 4I = 0 (eq. 1)
We also know that there were a total of 20 questions on the quiz, so we have the equation:
C + I + B = 20 (eq. 2)
We want to find the value of C, so let's solve this system of equations.
From eq. 1, we can rearrange it as:
6C = 4I
Simplifying it further by dividing both sides by 2, we have:
3C = 2I (eq. 3)
Next, let's substitute eq. 3 into eq. 2:
C + I + B = 20
3C/2 + C + B = 20
(3C + 2C)/2 + B = 20
5C/2 + B = 20
Rearranging this equation, we get:
5C + 2B = 40 (eq. 4)
Now, we can solve equations 3 and 4 simultaneously to find the values of C and B.
Multiply eq. 3 by 5/3 to make the coefficients of C the same:
5C/3 = 10I/3
Substitute this value into eq. 4:
(5C/3) + 2B = 40
(10I/3) + 2B = 40
Multiplying through by 3 to remove the fractions, we have:
5C + 6B = 120 (eq. 5)
Now we can solve equations 3 and 5 simultaneously.
From eq. 5, rearrange it as:
5C = 120 - 6B
Substitute this into eq. 3:
120 - 6B = 2I
60 - 3B = I (eq.6)
Now we have two equations to solve simultaneously:
60 - 3B = I (eq. 6)
3C = 2I (eq. 3)
Let's look at some possible values for B and I:
If B = 0, then I = 60, but this is not a valid solution since there are only 20 questions in total.
If B = 1, then I = 57, but this is also not a valid solution.
If B = 2, then I = 54, still not a valid solution.
If B = 3, then I = 51, which means C = 34.
Therefore, Bernard answered 34 questions correctly.
(b) We know that Raymond scored 16 for the quiz, and the number of questions he answered correctly is the same as the questions he answered incorrectly. Let's call this number X.
So the equation is:
6X - 4X = 16
Simplifying this equation, we have:
2X = 16
Dividing both sides by 2, we find:
X = 8
Now we know that Raymond answered 8 questions correctly and 8 questions incorrectly. Let's call the number of questions left blank Y.
So the equation is:
8 + 8 + Y = 20
Simplifying this equation, we have:
16 + Y = 20
Subtracting 16 from both sides, we find:
Y = 4
Therefore, Raymond left 4 questions blank.
To find the number of questions Bernard answered correctly and the number of questions Raymond left blank, we can set up equations based on the given information.
(a) Let's assume that Bernard answered x questions correctly. Since he answered all 20 questions, the number of questions answered incorrectly would be (20 - x).
The score for answering x questions correctly would be 6 points per question, so the total points earned for correct answers would be 6x.
The score for answering (20 - x) questions incorrectly would be -4 points per question, so the total points deducted for incorrect answers would be -4(20 - x).
Since the total score is zero, we can set up the equation:
6x - 4(20 - x) = 0
Solving this equation will give us the value of x, which represents the number of questions Bernard answered correctly.
(b) Let's assume that Raymond answered y questions correctly. Since the number of questions he answered incorrectly is the same as the number of questions answered correctly, the total number of questions answered correctly and incorrectly would be 2y.
The number of questions left blank can be found by subtracting the total answered questions (2y) from the total number of questions (20):
20 - 2y
The score for answering y questions correctly would be 6 points per question, so the total points earned for correct answers would be 6y.
The score for answering y questions incorrectly would be -4 points per question, so the total points deducted for incorrect answers would be -4y.
The score for leaving (20 - 2y) questions blank would be 0 points.
Since the total score is 16, we can set up the equation:
6y - 4y + 0 = 16
Solving this equation will give us the value of y, which represents the number of questions Raymond answered correctly, and also the number of questions he answered incorrectly.
Chrissy went to the store to buy some art supplies. She spent 1/5 of her money on paint and 1/3 of her money on paper. What fraction of her money did she spend?(1 point) Responses 23 2 thirds 8/15 8 over 15 7/15 7 over 15 2/15
To determine the fraction of Chrissy's money that she spent, we need to find a common denominator for the fractions 1/5 and 1/3. The least common multiple (LCM) of 5 and 3 is 15.
Now let's convert both fractions to have a denominator of 15:
1/5 = 3/15
1/3 = 5/15
Adding these fractions, we get:
3/15 + 5/15 = 8/15
Therefore, Chrissy spent 8/15 of her money.
James and Luke took a three-day hike along the Appalachian Trail. The first day they hiked 416 miles, the second day they hiked 323 miles, and the third day they hiked 423 miles. What total distance did the boys hike? You must type your response as a simplified mixed number. To type your fraction, click the box below. Type the whole number first. Then, select the fraction button where you see an x to the left of a fraction bar. Use your mouse or the up and down arrows on your keyboard to move between the numerator and denominator. The link below is a screen shot of the button you want to select.
To find the total distance James and Luke hiked, we need to add up the distances they hiked each day.
416 miles (first day) + 323 miles (second day) + 423 miles (third day) = 1162 miles.
Therefore, the boys hiked a total distance of 1162 miles.
James and Luke took a three-day hike along the Appalachian Trail. The first day they hiked 4 1/6 miles, the second day they hiked 3 2/3 miles, and the third day they hiked 4 2/3 miles. What total distance did the boys hike? You must type your response as a simplified mixed number. To type your fraction, click the box below. Type the whole number first. Then, select the fraction button where you see an x to the left of a fraction bar. Use your mouse or the up and down arrows on your keyboard to move between the numerator and denominator. The link below is a screen shot of the button you want to select.
To find the total distance James and Luke hiked, we need to add up the distances they hiked each day.
4 1/6 miles (first day) + 3 2/3 miles (second day) + 4 2/3 miles (third day)
Let's convert these mixed numbers to improper fractions:
4 1/6 = (4 * 6 + 1)/6 = 25/6
3 2/3 = (3 * 3 + 2)/3 = 11/3
4 2/3 = (4 * 3 + 2)/3 = 14/3
Now we can add these fractions:
25/6 + 11/3 + 14/3
To add these fractions, we need a common denominator, which is 6 in this case. So let's convert 11/3 and 14/3 to have a denominator of 6:
11/3 = (11 * 2)/ (3 * 2) = 22/6
14/3 = (14 * 2)/ (3 * 2) = 28/6
Now let's add these fractions:
25/6 + 22/6 + 28/6 = (25 + 22 + 28)/6 = 75/6
Since we need to express the answer as a simplified mixed number, let's divide the numerator by the denominator and express any remainder as a fraction:
75 ÷ 6 = 12 with a remainder of 3
So the total distance James and Luke hiked is 12 3/6 miles. To simplify this mixed number, we can reduce the fraction:
3/6 = 1/2
Therefore, the total distance they hiked is 12 1/2 miles.
Charlie's horse, Star, was getting too heavy eating 3 1/2 pounds of horse feed twice a day. Charlie reduced Stars feed by 3/4 of a pound at each feeding. How much is Star now eating each day? You must type your response as a simplified mixed number. To type your fraction, click the box below. Type the whole number first. Then, select the fraction button where you see an x to the left of a fraction bar. Use your mouse or the up and down arrows on your keyboard to move between the numerator and denominator. The link below is a screen shot of the button you want to select.
To find out how much horse feed Star is now eating each day, we need to subtract the amount Charlie reduced from the original amount.
Original amount: 3 1/2 pounds twice a day
Amount reduced: 3/4 of a pound at each feeding
Let's convert the mixed number 3 1/2 to an improper fraction:
3 1/2 = (3 * 2 + 1)/2 = 7/2
So, the original amount of horse feed each day was 7/2 pounds.
Now, let's subtract 3/4 pounds from the original amount:
7/2 - 3/4 = (7 * 2 - 3)/4 = 11/4
Therefore, Star is now eating 11/4 pounds of horse feed each day.
To express this as a simplified mixed number, let's divide the numerator by the denominator and express any remainder as a fraction:
11 ÷ 4 = 2 with a remainder of 3
So the final answer is 2 3/4 pounds.
Therefore, Star is now eating 2 3/4 pounds of horse feed each day.
Jamal made a salad that uses 3/4 of a pound of lettuce, 1 1/2 pounds of tomatoes, and 5/6 of a pound of cheese. In order to see how much the finished salad would weigh, what operation would you use?(1 point) Responses Division Division Subtraction Subtraction Multiplication Multiplication Addition
To find out how much the finished salad would weigh, we need to calculate the sum of the weights of the lettuce, tomatoes, and cheese.
Since we want to determine the total weight of the salad, we should use the ADDITION operation. By adding the weights of the lettuce, tomatoes, and cheese together, we can find the total weight of the salad.
nspired by a video, Brooke decided to try a Filipino chicken recipe. The recipe requires 212 pounds of chicken. Brooke bought 534 pounds of chicken. How many pounds of chicken remain unused? Drag and drop the correct numbers and operation into the appropriate boxes below to set up the problem and show the solution. Not all answer choices will be used. (1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Response area Response area Response area =
To find out how many pounds of chicken remain unused, we need to subtract the amount of chicken Brooke used (212 pounds) from the amount of chicken she bought (534 pounds).
534 pounds - 212 pounds =
322 pounds
Therefore, Brooke has 322 pounds of chicken remaining unused.
nspired by a video, Brooke decided to try a Filipino chicken recipe. The recipe requires 2 1/2 pounds of chicken. Brooke bought 5 3/4 pounds of chicken. How many pounds of chicken remain unused? Drag and drop the correct numbers and operation into the appropriate boxes below to set up the problem and show the solution. Not all answer choices will be used. (1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Response area Response area Response area =
To find out how many pounds of chicken remain unused, we need to subtract the amount of chicken Brooke used (2 1/2 pounds) from the amount of chicken she bought (5 3/4 pounds).
5 3/4 pounds - 2 1/2 pounds =
To subtract mixed numbers, we need to borrow/regroup from the whole number part:
5 3/4 pounds - 2 1/2 pounds =
(5 - 2) + (3/4 - 1/2) pounds =
3 + 1/4 pounds =
Therefore, Brooke has 3 1/4 pounds of chicken remaining unused.
Identify the units in the following word problem: During their family vacation, the Lawson family bought 14 2/3 gallons of gasoline for their car. At the end of the trip, they had 5 2/5 gallons left. How much gas did they use during the trip? (1 point) Responses trip trip car car vacation vacation gallons
The units in the word problem are gallons. The problem mentions the Lawson family buying and using gallons of gasoline during their family vacation.
Question Sarah's mom baked 2 5/6 pounds of french fries for lunch. Sarah ate 1 2/3 pounds of french fries and her mom ate the rest. What operation would you use to find the amount of french fries Sarah's mom ate?(1 point) Responses multiplication multiplication addition addition division division subtraction subtraction
To find the amount of french fries Sarah's mom ate, we need to subtract the amount of french fries Sarah ate from the total amount baked by Sarah's mom.
So, we would use the SUBTRACTION operation to find the amount of french fries Sarah's mom ate.
Beginning at 8:30 am, tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 15 minutes. Tours for the White House leave every 20 minutes. How often do the tours leave at the same time?(1 point) Responses every 15 minutes every 15 minutes every 30 minutes every 30 minutes every 35 minutes every 35 minutes every 60 minutes every 60 minutes
To determine how often the tours leave at the same time, we need to find the least common multiple (LCM) of 15 minutes and 20 minutes, which represents the interval at which the tours coincide.
The LCM of 15 and 20 is 60.
Therefore, the tours leave at the same time every 60 minutes.
Select all statements below which are true (1 point) Responses Ratios and proportions compare items with the same labels. Ratios and proportions compare items with the same labels. Ratios and proportions compare items with different labels. Ratios and proportions compare items with different labels. Ratios express the relationship between two or more items. Ratios express the relationship between two or more items. Ratios express the relationship between only one item.
Ratios and proportions compare items with the same labels.
Ratios express the relationship between two or more items.
So the correct statements are:
- Ratios and proportions compare items with the same labels.
- Ratios express the relationship between two or more items.
r Toccare and Anesia have glitter markers in a ratio of 2:3. They have a total of 30 glitter markers. How many glitter markers does Anesia have? (1 point) Responses 6 6 12 12 18 18 24 24
Search instead for Tocarre and Anesia have glitter markers in a ratio of 2:3. They have a total of 30 glitter markers. How many glitter markers does Anesia have? (1 point) Responses 6 6 12 12 18