Math Magic: Finding The Average Quiz

Explanation
To calculate the average weight of the bears, we need to add up the weights of all the bears and then divide by the total number of bears.Total weight = 524 lbs + 756 lbs + 982 lbs = 2262 lbsThere are three bears in total.Average weight = Total weight / Number of bearsAverage weight = 2262 lbs / 3Average weight ≈ 754 lbs

Explanation
To find the fifth score, we first need to calculate the sum of the four given scores:90 + 88 + 92 + 80 = 350We know the average of the five scores is 85, and the sum of all five scores is 85 multiplied by 5:85 * 5 = 425Now, we can subtract the sum of the four given scores from the total sum of the five scores to find the fifth score:425 - 350 = 75So, the fifth score is 75.

Explanation
Let's solve this to find the average of the remaining 7 numbers:
Total Sum: Since the average of 8 numbers is 25, the total sum of all 8 numbers is: Average * Number of elements = 25 * 8 = 200.
Remove the 50: We know one of the numbers is 50. We need to find the average excluding this number.
Remaining Numbers' Sum: Subtract the value of the removed number (50) from the total sum: 200 (total sum) - 50 (removed number) = 150.
Average of Remaining: Now, divide the remaining sum by the number of remaining elements (7): 150 (remaining sum) / 7 (remaining elements) = 21.43 (approximately).
Therefore, the average of the remaining 7 numbers is approximately 21. 

Explanation
Let's say we want to find the new average X after all 6 games:
Total Points Needed: If X is the new average for all 6 games, the total points needed for all games would be X * 6 (number of games).
Points from First 5 Games: We already know the average for the first 5 games (90 points) and the number of games (5). So, the total points from the first 5 games are 5 * 90 = 450 points.
Points Needed for New Average: Subtract the points already scored in the first 5 games from the total points needed for the new average (considering all 6 games): X * 6 (total points needed) - 450 (points from first 5 games) = total points needed for the new average with all 6 games.
Since we know the score for the sixth game (110 points), we can replace "total points needed for the new average with all 6 games" with 110 points.
This becomes: X * 6 - 450 = 110
Solving for X (new average):
X * 6 = 560
X = 560 / 6
X = 93.33 (approximately)
X=93

Explanation
To find the average cost, we need to add the prices of the three cars and then divide by the number of cars.
Total Cost: $10,100 + $7,800 + $12,400 = $30,300
Number of Cars: 3
Average Cost: $30,300 (total cost) / 3 (number of cars) = $10,100 (average cost)

Explanation
Total Number of Students: Add the number of students from each school: 687 (Paul's) + 841 (Nicole's) + 497 (Kurt's) = 2025 students.
Number of Schools: There are 3 schools (Paul's, Nicole's, and Kurt's).
Average Number of Students: Divide the total number of students by the number of schools
2025 students / 3 schools = 675 students/school (average).
Therefore, the average number of students at these schools is approximately 675.

Explanation
Total Number of Houses: Add the number of houses on each street: 43 houses + 26 houses + 18 houses + 37 houses = 124 houses.
Number of Streets: There are 4 streets mentioned.
Average Number of Houses per Street: Divide the total number of houses by the number of streets:
124 houses / 4 streets = 31 houses/street (average).
Therefore, the average number of houses per street in this neighborhood is 31.

Explanation
Total Number of Stickers: Add the number of stickers each girl has: 365 (Lynn) + 343 (Bridget) + 219 (Karen) + 37 (Liz) = 964 stickers.
Number of Girls: There are 4 girls (Lynn, Bridget, Karen, and Liz).
Average Number of Stickers: Divide the total number of stickers by the number of girls
964 stickers / 4 girls = 241 stickers/girl (average).
Therefore, the average number of stickers in their collection is 241 per girl.

Explanation
Using the average formula
Since we have the number of libraries (4) and the individual book counts can be treated as a set of data points, we can directly use the average formula:
Average = (Sum of data points) / Number of data points
Here, the data points are the book counts (10,890, 14,594, 9,786, 12,754).
Average = (10,890 + 14,594 + 9,786 + 12,754) / 4
Average Number of Books: Divide the total number of books by the number of libraries: 48,024 books / 4 libraries = 12,006 books/library (average).
Therefore, the average number of books in the libraries is 12,006.

Explanation
To find the average price of the candy bars, we need to follow these steps:
Total Price: Add the prices of all five candy bars: 45 cents + 65 cents + 90 cents + 85 cents + 75 cents = 360 cents.
Conversion to Dollars (Optional): We can find the average in cents, but since the question asks for the average price in dollars, we need to convert cents to dollars. There are 100 cents in 1 dollar.
Average Price (in cents): Divide the total price (in cents) by the number of candy bars: 360 cents / 5 bars = 72 cents/bar (average).
Average Price (in dollars): Divide the average price in cents by 100 (conversion rate): 72 cents / 100 cents/dollar = $0.72/bar (average).
Therefore, the average price of a candy bar is $0.72.