Question

There is a total of 190 men, women and children on a train.

The ratio of men to women is 3 : 4.
The ratio of women to children is 8: 5.
How many men are on the train?

Answer 1

Let's start by assigning variables to the unknown quantities. Let M be the number of men, W be the number of women, and C be the number of children. We know that:

M + W + C = 190 ---(1)

M/W = 3/4 ---(2)

W/C = 8/5 ---(3)

From equation (2), we can write M = 3W/4.

Substituting this into equation (3), we get:

(3W/4)/C = 8/5

Simplifying this expression, we get:

C = 15W/32 ---(4)

Now we can substitute (2) and (4) into (1) and solve for W:

M + W + (15W/32) = 190

Multiplying both sides by 32, we get:

32M + 32W + 15W = 6080

Substituting M = 3W/4, we get:

24W + 32W + 15W = 6080

71W = 6080

W = 85

Now that we know there are 85 women on the train, we can use equation (2) to find the number of men:

M/W = 3/4

M/85 = 3/4

M = (3/4) x 85

M = 63.75

Since we can't have a fraction of a person, we round up to the nearest whole number, giving us:

M = 64

Therefore, there are 64 men on the train.

Answer 2

42 men

Explanation:

Let's use algebra to solve this problem. We can start by using the ratio of men to women to find how many men and women are on the train combined.

If the ratio of men to women is 3:4, then we can express the number of men as 3x and the number of women as 4x, where x is a common factor.

Next, we can use the ratio of women to children to find how many women and children are on the train combined.

If the ratio of women to children is 8:5, then we can express the number of women as 8y and the number of children as 5y, where y is a common factor.

We know that the total number of people on the train is 190, so we can write an equation:

3x + 4x + 8y + 5y = 190

Simplifying the equation, we get:

7x + 13y = 190

We want to find the value of x, which represents the number of men. We can use the ratio of men to women to write:

3x/4x = 3/4

Simplifying the equation, we get:

3x = (3/4)4x

3x = 3x

This tells us that the ratio of men to women is independent of the value of x. We can use this information to solve for x.

Since 7x + 13y = 190, we know that y = (190 - 7x)/13. Substituting this value of y into the equation for the number of women, we get:

4x = 8y

4x = 8(190 - 7x)/13

Multiplying both sides by 13, we get:

52x = 1520 - 56x

Simplifying the equation, we get:

108x = 1520

Dividing both sides by 108, we get:

x = 14.074

Since we are looking for a whole number of men, we can round down to 14. Therefore, there are 3x = 3(14) = 42 men on the train.