Answer:
Population A has 4590 and population B has 1520 bacteria
Explanation:
Let’s mark bacteria:
a - bacteria from population A
b - bacteria from population B
Every bacteria a needs 4 units of the first nutrient and every bacteria b needs 1 unit of the same nutrient, so we can write it down as:
4*a + 1*b = 19880
Let’s do the same for the second nutrient. Every bacteria a needs 5 units of the second nutrient and every bacteria b needs 6 units of the second nutrient:
5*a + 6*b = 32070
Now there are two equations and two unknowns. From the first equation, we can separate b:
b = 19880 - 4a
Let’s place this b to the second equation:
5a + 6*(19880 - 4a) = 32070
5a + 119280 - 24a = 32070
119280 - 32070 = 24a - 5a
19a = 87210
a = 4590
This can be brought back to: b = 19880 - 4a
b = 1520