In a group of m men, b men earn D dollars per week and the rest earn half that amount each. Represent the total number of dollars paid to these men in a week.
P.S. Whenever i try solving this problem i get 3/2D(b+m) Could you kindly tell what i am doing wrong?
b men earning D dollars = bD
remaining men = m-b each earning D/2
so they earn D/2(m - b) = mD/2 - bD/2
total = bD + mD/2 - bD/2
= 2bD/2 + mD/2 - bD/2 , using a common denominator
= bD/2 + mD/2
= D/2(b+m) , using a common factor of D/2
which is B
D/2 is the same as (1/2)D
The answer choices for this problem were:
(A) bD+b-m
(B) 1/2D(b+m)
(C) 3/2D+mD
(D) 3/2D(b+m)
(E) bD+1/2mD
The answer to this problem is "B", but I don't understand how they got it.
To represent the total number of dollars paid to these men in a week, we need to calculate the earnings for each group separately and then sum them up.
Let's break down the calculation step by step:
1. Number of men earning D dollars per week: b
2. Number of men earning half of D dollars per week: m - b
Next, we calculate the total earnings for each group separately:
1. Total earnings for men earning D dollars per week: b * D
2. Total earnings for men earning half of D dollars per week: (m - b) * (D/2)
Now, let's add these earnings together to get the total number of dollars paid to these men in a week:
Total = (b * D) + ((m - b) * (D/2))
To simplify this expression, we can multiply the second term by 2/2:
Total = (b * D) + ((m - b) * (D * 2/2))
Total = (b * D) + ((m - b) * (2D/2))
Total = (b * D) + ((m - b) * D)
Now, let's distribute the D:
Total = bD + mD - bD
Total = mD
So, the correct representation for the total number of dollars paid to these men in a week is mD, not 3/2D(b + m).
To determine where you went wrong in your calculation, let's break down the problem step by step.
You have a group of m men. Out of these men, b men earn D dollars per week, and the remaining men earn half that amount each.
Let's calculate the total number of dollars paid to these men in a week.
To do this, we need to determine the earnings of each group of men separately and then add them up.
Earnings of the b men:
The b men earn D dollars per week, so the total earnings of b men can be calculated as b * D.
Earnings of the remaining men:
The remaining men earn half the amount earned by the b men. So, each of these men earns D/2 dollars per week. As there are m men in total and b men are already accounted for, the number of remaining men is (m - b). Therefore, the total earnings of the remaining men can be calculated as (m - b) * (D/2).
Now, to find the total number of dollars paid to all the men in a week, we sum up the earnings of the b men and the remaining men:
Total earnings = b * D + (m - b) * (D/2)
Simplifying this expression, we get:
Total earnings = bD + m(D/2) - b(D/2)
Total earnings = bD + (mD/2) - (bD/2)
Total earnings = bD/2 + mD/2
Total earnings = (b + m)D/2
So, the correct expression for the total number of dollars paid to the men in a week is (b + m)D/2, not 3/2D(b + m).