Math Magic: Finding The Average Quiz

2.

The average of five test scores is 85. If four of the scores are 90, 88, 92, and 80, what is the fifth score?

75
85
90
86

Correct Answer

A. 75

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.

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7

3.

The average of a set of 8 numbers is 25. If one of the numbers is 50, what is the average of the remaining 7 numbers? (Approx)

25
21
24
23

Correct Answer

A. 21

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.

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2

4.

The average score of a basketball team for the first five games is 90 points. If the team scores 110 points in the sixth game, what is the new average score? (Approx.)

92
94
93
98

Correct Answer

A. 93

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

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2

5.

Three new cars cost $10,100; $7,800 and $12,400. What is the average cost for these cars?

$10,100
$10,000
$10,500
$10,800

Correct Answer

A. $10,100

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)

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2

6.

What is the average of the numbers 4, 8, 12, and 16?

8
10
12
14

Correct Answer

A. 10

Explanation

To find the average, also known as the mean, you sum up all the given numbers and then divide that total by the number of values in the set. In this case, the sum of 4, 8, 12, and 16 is 40. There are four numbers in the set, so you divide the sum of 40 by 4, which equals 10.

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4

7.

One street in our neighborhood has 43 houses, one has 26, one has 18, and one has 37. What is the average number of houses per street?

30
28
31
32

Correct Answer

A. 31

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.

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1

8.

Lynn has 365 stickers in her collection. Bridget has 343 and Karen has 219 and Liz has 37. What is the average number of stickers?

241
266
254
270

Correct Answer

A. 241

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.

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9.

Four libraries each have this many books: 10,890; 14,594; 9,786; 12,754 What is the average number of books for the libraries?

12,000
12,006
12,026
11,860

Correct Answer

A. 12,006

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.

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10.

Doug found five different candy bars with these prices: 45,65,90,85 and 75 cents. What was the average price?

$0.70
$0.84
$0.72
$0.75

Correct Answer

A. $0.72

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.

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Math Magic: Finding The Average Quiz

One bear at the zoo weighs 524 lbs. The others weigh 756 lbs and 982 lbs. What is their average weight?

Quiz Preview

The average of five test scores is 85. If four of the scores are 90, 88, 92, and 80, what is the fifth score?

The average of a set of 8 numbers is 25. If one of the numbers is 50, what is the average of the remaining 7 numbers? (Approx)

The average score of a basketball team for the first five games is 90 points. If the team scores 110 points in the sixth game, what is the new average score? (Approx.)

Three new cars cost $10,100; $7,800 and $12,400. What is the average cost for these cars?

What is the average of the numbers 4, 8, 12, and 16?

One street in our neighborhood has 43 houses, one has 26, one has 18, and one has 37. What is the average number of houses per street?

Lynn has 365 stickers in her collection. Bridget has 343 and Karen has 219 and Liz has 37. What is the average number of stickers?

Four libraries each have this many books: 10,890; 14,594; 9,786; 12,754 What is the average number of books for the libraries?

Doug found five different candy bars with these prices: 45,65,90,85 and 75 cents. What was the average price?