Algebra problems?

Question

In a group of 180 persons composed men, women, and children, there are twice as many men as women, and three times as many women as children. How many are there each?

In 8 years, a will be 3 years older than twice her present age. How old is she now?

If a certain number is added to 36, the result is the same as if the number were multiplied by 4. What is the number?

Answer 1

Let the number of men = m, number of women = w and children = c. m + w + c = 180 because that's the total number of people.
There are twice as many men as women, so m = 2w.
There are three times as many women as children, so w = 3c.
Use substitution:
m + w + c = 180
w = 3c
m = 2w = 2(3c) = 6c
So subbing in these values:
6c + 3c + c = 180
10c = 180
c = 18.
Plug this value into the other equations to solve for m and w:
m = 6c = 6 x 18 = 108
w = 3c = 3 x 18 = 54
=> There are 18 children, 54 women and 108 men.
Double check by making sure that there are twice as many men as women, three times as many women as children, and that the total amount of people is 180.

Let the person's age now be x. In 8 years, the person will be (x + 8) years old. This is 3 more than twice her current age, so we can write out an equation and solve:
x + 8 = 2x + 3
x + 8 - x = 2x + 3 - x
8 = x + 3
8 - 3 = x + 3 - 3
x = 5
=> Her current age is 5.
Double check to make sure that in 8 years her age will be 3 more than twice her current age.

Let this certain number be y. Write an equation for it:
y + 36 = 4y
y + 36 - y = 4y - y
36 = 3y
y = 12
=> This number is 12.
Double check by adding 36 to this number and making sure that it's the same as if you multipled the number by 4.

Answer 2

If A= no of men
then no of women = 1/2 A
then no of children = 1/3(1/2 A) = 1/6 A
So, A + 1/2 A + 1/6 A = 180
10/6 A = 180
A = 108
men = 108
women = 54
childrean = 18

a + 8 years - 3 years older = 2a (present)
a +5 = 2a
a = 5 age

x + 36 = 4x
3x =36
x = 12

Answer 3

x = number of children
3x = number women
6x = number of men
10x = 180
x=18 = children
3x = 54 = women
6x =108 = men

let x = present age
x+8 = 2x=3
x = 5

36+x = 4x
36 = 3x
12 = x

Answer 4

let x be numbers of children.
x+3x+6x=180
10x=180
x=18
There are 18children,54women,108men.

let x be her present age.
x+8=2x+3
x=5
She is 5years old.

let the certain number be x.
x+36=4x
3x=36
x=12
The number is 12.