1).Last year, a shopkeeper sold an average of 7 cartons of apples from january to april. He sold an average of 9 cartons of apples from june till end of the year. What is the total number of cartons he sold in the 11 months? if each carton contains 66 apples,what is the average number of apples sold per month?
2) Ameter records voltages between 0 volts and 20 volts. If the average value for three readings on the meter was 16 volts, what is the smallest possible reading, in volts?
3) The average of a set of 50 numbers is 38. The numbers of the set, namely 45 and 55 are discarded. What is the average of the remaining set of numbers?
1)
4 months @ 7 = 28 cartons
8 months @ 9 = 72 cartons
(assuming the year has 12 months instead of 11)
average apples sold per month is 100*66/12 = 550
2)
since the sum is 48, and no single reading is over 20, then the smallest must be at least 8.
3)
sum of numbers is 50*38 = 1900
new sum, less discarded values = 1800
new average is 1800/48 = 37.5
1) To find the total number of cartons sold in 11 months, we need to calculate the sum of the cartons sold in each individual month and then add them together.
First, let's calculate the cartons sold from January to April:
- The shopkeeper sold an average of 7 cartons per month.
- There are a total of 4 months from January to April.
- So, the total cartons sold from January to April would be 7 cartons/month * 4 months = 28 cartons.
Next, let's calculate the cartons sold from June till the end of the year:
- The shopkeeper sold an average of 9 cartons per month.
- There are a total of 7 months from June till the end of the year.
- So, the total cartons sold from June till the end of the year would be 9 cartons/month * 7 months = 63 cartons.
Now, let's find the total cartons sold in the 11 months by adding the two results:
Total cartons sold = cartons sold from January to April + cartons sold from June till the end of the year = 28 cartons + 63 cartons = 91 cartons.
Since each carton contains 66 apples, to find the total number of apples sold, we can multiply the total number of cartons sold by 66:
Total number of apples sold = Total cartons sold * 66 = 91 cartons * 66 = 6,006 apples.
To find the average number of apples sold per month, we need to divide the total number of apples sold (6,006 apples) by the number of months (11 months):
Average number of apples sold per month = Total number of apples sold / Number of months = 6,006 apples / 11 months = 546 apples per month (rounded to the nearest whole number).
2) To find the smallest possible reading, we need to consider that the average value of three readings is 16 volts.
Let's assume the smallest reading is x volts. Then, the other two readings must be greater than x in order to achieve an average value of 16 volts.
So, we have the following inequality: (x + (x+a) + (x+b)) / 3 = 16.
Here, a and b are the additional voltage values for the second and third readings.
Simplifying the equation: (3x + a + b) / 3 = 16.
Multiplying both sides of the equation by 3: 3x + a + b = 48.
Subtracting a and b from both sides: 3x = 48 - a - b.
To find the smallest possible value for x, we want to minimize the values of a and b. Therefore, we set a = 0 (minimum value) and b = 0 (minimum value).
Now, the equation becomes: 3x = 48 - 0 - 0.
Simplifying further: 3x = 48.
Finally, dividing both sides of the equation by 3, we find the smallest possible value for x:
x = 48 / 3 = 16 volts.
So, the smallest possible reading on the meter is 16 volts.
3) The average of a set of 50 numbers is 38. Two numbers, 45 and 55, are discarded from the set. We want to find the average of the remaining set of numbers.
To find the sum of the remaining set of numbers, we multiply the average (38) by the total number of numbers (50) in the original set:
Sum of the original set = Average * Total number of numbers = 38 * 50 = 1900.
Now, we need to subtract the numbers that were discarded (45 and 55) from the total sum of the original set:
Sum of the remaining set = Sum of the original set - Sum of discarded numbers = 1900 - (45 + 55) = 1900 - 100 = 1800.
To find the average of the remaining set of numbers, we divide the sum of the remaining set (1800) by the number of remaining numbers (50 - 2 = 48):
Average of the remaining set = Sum of the remaining set / Number of remaining numbers = 1800 / 48 = 37.5.
Therefore, the average of the remaining set of numbers after discarding 45 and 55 is 37.5.