Combined, there are 184

​Asians, Africans,​ Europeans, and Americans in a village.The number of Asians exceeds the number of Africans and Europeans by 61. The difference between the number of Europeans and Americans is 11. If the number of Africans is​ doubled, their population exceeds the number of Europeans and Americans by 15.
Determine the number of​ Asians, Africans,​ Europeans, and Americans in this village.

So how many Asians:
Africans:
Europeans:
Americans in Village:

If i create this formula,
Assign letters to each race. These are your variables.
Asians = A
Africans = F
Europeans = E
Americans = M

A + F + E + M = 184
Is this a good way to start the problem?

You are told the number of Asians exceeds the number of Africans and Europeans by 61.

Therefore A - 61 = F + E

Kind of not sure where to go from here.

Yes, that is the start. Write all four equations in that matrix form.

A + F + E + M = 184
A - F - E + 0M = 61
0A + 0F + E - M = 11
2A + 0F -E - M = 15

There are several methods, including row reduction.

Yes, assigning letters to each race as variables is a good way to start solving the problem. So, let's continue with the information given.

We have the equation: A + F + E + M = 184 (Equation 1)

We are also told that the number of Asians exceeds the number of Africans and Europeans by 61. So we can write this as an equation:

A = F + E + 61 (Equation 2)

Next, we are given that the difference between the number of Europeans and Americans is 11. This gives us another equation:

E - M = 11 (Equation 3)

Finally, we are told that if the number of Africans is doubled, their population exceeds the number of Europeans and Americans by 15. Mathematically, this can be represented as:

2F = E + M + 15 (Equation 4)

We now have a system of four equations (Equations 1, 2, 3, and 4) with four variables (A, F, E, and M). We can solve this system of equations to find the values of A, F, E, and M.

One way to solve this system of equations is by substitution or elimination. However, it can be quite complex and time-consuming. Another approach is to use online calculators or matrix methods to solve the system of equations.

You can use a matrix calculator or an algebraic solver to enter the equations and find the values of A, F, E, and M. This will give you the number of Asians, Africans, Europeans, and Americans in the village.