In the United States, the highest incidence of fraternal twin births occurs among Asian-Americans, then African-Americans, then Caucasians. Of every 16200 births, the total number of fraternal twin births for all three is 778, where there are 195 more for Asian-Americans than African-Americans and 242 more for Asian-Americans than Caucasians. Determine the number for each race.
Out of every 16200 births, there are_____? sets of Asian-American twins,_____? sets of African-American twins, and _____? sets of Caucasian twins.
as + af + ca = 778
af = as -195
ca = as -242
so
as + as-195 + as-242 = 778
3 as = 1215
as = 405
you can take it from there I think.
I got 405, 210, and 163.
Good.
To determine the number of sets of twin births for each race, we can use a system of equations.
Let's define the variables:
Let A = number of sets of Asian-American twins
Let B = number of sets of African-American twins
Let C = number of sets of Caucasian twins
From the given information, we have the following equations:
1. The total number of sets of twin births for all three races is 778:
A + B + C = 778
2. Among Asian-Americans, there are 195 more sets of twin births than among African-Americans:
A = B + 195
3. Among Asian-Americans, there are 242 more sets of twin births than among Caucasians:
A = C + 242
Now we can solve this system of equations.
First, substitute Equation 2 into Equation 1 to eliminate A:
(B + 195) + B + C = 778
2B + C = 583
Next, substitute Equation 3 into Equation 1 to eliminate A:
(C + 242) + B + C = 778
2C + B = 536
Now we have a system of two equations with two variables:
2B + C = 583
2C + B = 536
Solve this system of equations using any method you prefer. One way to solve it is by substitution:
From Equation 2, we can express B in terms of C:
B = C + 242
Substitute this into Equation 1:
2C + (C + 242) = 536
3C + 242 = 536
3C = 536 - 242
3C = 294
C = 294 / 3
C = 98
Now substitute C back into the expression for B:
B = C + 242
B = 98 + 242
B = 340
Finally, substitute the values of B and C into Equation 1 to find A:
A + B + C = 778
A + 340 + 98 = 778
A = 778 - 340 - 98
A = 340
Therefore, the number of sets of twin births for each race is as follows:
Asian-Americans: 340 sets
African-Americans: 340 - 195 = 145 sets
Caucasians: 98 sets
So, out of every 16200 births, there are 340 sets of Asian-American twins, 145 sets of African-American twins, and 98 sets of Caucasian twins.