In a group og 180 persons composed of men,women,and children , there are twice as many men as women, and three times as many children. how many are there of each?
Thx it really helped
Let's set up some equations to solve this problem step-by-step:
Let M be the number of men, W be the number of women, and C be the number of children.
We are given three pieces of information:
1. There are twice as many men as women, so M = 2W.
2. There are three times as many children, so C = 3W.
3. The total number of persons is 180, so M + W + C = 180.
Step 1: Substitute the value of M from equation 1 into equation 3.
2W + W + 3W = 180.
6W = 180.
Step 2: Solve for W.
Divide both sides of the equation by 6:
W = 180 / 6.
W = 30.
Step 3: Substitute the value of W from step 2 into equations 1 and 2 to find the values of M and C.
M = 2W = 2 × 30 = 60.
C = 3W = 3 × 30 = 90.
So, there are 60 men, 30 women, and 90 children.
To solve this problem, we can use a system of equations. Let's assign variables to each group:
- Let "x" represent the number of women
- Since there are twice as many men as women, the number of men will be 2x
- Since there are three times as many children, the number of children will be 3x
We know that the total number of people in the group is 180. So, we can write the equation:
x + 2x + 3x = 180
Combining like terms:
6x = 180
To find the value of "x," we divide both sides of the equation by 6:
x = 180 / 6
x = 30
Now that we know the number of women (x = 30), we can calculate the number of men and children:
- Number of men: 2x = 2(30) = 60
- Number of children: 3x = 3(30) = 90
Therefore, in the group of 180 people, there are 30 women, 60 men, and 90 children.
If there are x women, then
x + 2x + 3x = 180
Solve for x, and then you can determine how many of each.