Mr. Bobby bought 50 shares at $60, and 2 months later purchased 25 shares a $56.at what price should he purchase 25 additional shares in order to have an average price $58 per share?
The average age of a family of 6 members is 25 years. The average of the family after a 45 years old members leaves is?
In a course a students final exam is weighted twice as heavily as his midterm exam.If a student receives a score of 84 on his final exam and 90 on his midterm exam ,what is the average for the course?
1) To find the price at which Mr. Bobby should purchase 25 additional shares, we need to use the concept of weighted average.
First, let's calculate the total investment Mr. Bobby made so far:
Total Investment = (Number of shares * Price per share) + (Number of shares * Price per share)
Total Investment = (50 shares * $60 per share) + (25 shares * $56 per share)
Total Investment = $3000 + $1400
Total Investment = $4400
Now, let's calculate the additional investment needed to achieve an average price of $58 per share:
Additional Investment = (Number of additional shares * Price per share)
Additional Investment = 25 shares * Price per share
Additional Investment = 25 shares * $x per share
To achieve an average price of $58 per share, the new total investment should be:
New Total Investment = Total Investment + Additional Investment
New Total Investment = $4400 + (25 shares * $x per share)
We can set up an equation to solve for x:
(4400 + (25x)) / (50 + 25) = 58
Simplifying the equation:
(4400 + 25x) / 75 = 58
4400 + 25x = 58 * 75
4400 + 25x = 4350
25x = 4350 - 4400
25x = -50
x = -50 / 25
x = -2
Therefore, Mr. Bobby should purchase 25 additional shares at a price of -$2 per share to achieve an average price of $58 per share. Note that a negative price is not practical in the real world scenario.
2) The average age of a family of 6 members is 25 years. If a 45-year-old member leaves the family, the total age of the remaining family members will decrease.
Before the member leaves, the total age of the family is:
Total Age = Average Age * Number of Members
Total Age = 25 years * 6 members
Total Age = 150 years
After the 45-year-old member leaves, the total age of the remaining family members will be:
New Total Age = Total Age - Age of the person leaving
New Total Age = 150 years - 45 years
New Total Age = 105 years
Now, let's calculate the new average age:
New Average Age = New Total Age / (Number of Members - 1)
New Average Age = 105 years / (6 members - 1)
New Average Age = 105 years / 5 members
New Average Age = 21 years
Therefore, the average age of the family after the 45-year-old member leaves is 21 years.
3) In a course where the final exam is weighted twice as heavily as the midterm exam, we can calculate the average score by using the concept of weighted average.
Let's assign weights to the exams:
Midterm Exam Weight = 1
Final Exam Weight = 2
Now, let's calculate the weighted average score:
Weighted Average = (Midterm Exam Score * Midterm Exam Weight) + (Final Exam Score * Final Exam Weight)
Weighted Average = (90 * 1) + (84 * 2)
Weighted Average = 90 + 168
Weighted Average = 258
The total weight is 1 + 2 = 3.
Final Average = Weighted Average / Total Weight
Final Average = 258 / 3
Final Average = 86
Therefore, the average for the course is 86.
To find the price at which Mr. Bobby should purchase 25 additional shares in order to have an average price of $58 per share, we can set up an equation.
Let x be the price at which he should purchase 25 additional shares.
The total cost of the initial 50 shares is 50 * $60 = $3000.
The total cost of the second 25 shares is 25 * $56 = $1400.
The total cost of the additional 25 shares is 25 * x = 25x.
The average price is given by the formula:
(3000 + 1400 + 25x) / (50 + 25 + 25) = $58
Simplifying the equation gives us:
(4400 + 25x) / 100 = $58
Multiply both sides by 100 to remove the denominator:
4400 + 25x = 5800
Subtract 4400 from both sides:
25x = 1400
Divide both sides by 25 to solve for x:
x = 56
Therefore, Mr. Bobby should purchase 25 additional shares at $56 each to have an average price of $58 per share.
To find the average of the family when a 45-year-old member leaves, we need to calculate the new sum of ages and divide it by the number of remaining family members.
Given that the average age of the family of 6 members is 25 years, the sum of ages would be 6 * 25 = 150 years.
When the 45-year-old member leaves, the sum of ages becomes 150 - 45 = 105 years.
Since there are 5 remaining family members, the new average age would be 105 / 5 = 21 years.
Therefore, the average of the family after the 45-year-old member leaves is 21 years.
To find the average score for the course, we need to account for the weight of the final exam and the midterm exam.
Given that the final exam is weighted twice as heavily as the midterm exam, we can assign weights of 2 to the final exam and 1 to the midterm exam.
If the student receives a score of 84 on the final exam and 90 on the midterm exam, we can calculate the average score using the formula:
Average score = (Score on final exam * weight of final exam + Score on midterm exam * weight of midterm exam) / (weight of final exam + weight of midterm exam)
Plugging in the values:
Average score = (84 * 2 + 90 * 1) / (2 + 1)
= (168 + 90) / 3
= 258 / 3
= 86
Therefore, the average score for the course would be 86.
#1: If the price is x, then we must have
50*60 + 25*56 + 25x = 58(50+25+25)
#2: (6*25-45)/5
#3: (90+2*84)/3