What are the equations for this word problem?

Question

Problem: There are two containers holding saline solution. The first container has a 10% concentration of saline, while the second container has a 16% concentration. The contents of the two containers are mixed, and the resulting solution is 220mL with a saline concentration of 12%. What was the volume of each of the two original containers' solutions?

Please give me the two equations to use to find the answer. If possible, explain why they are the right equations to use. ty :)

Answer 1

Let x = amount of solution in container 1
and y = amount of solution in container 2

Now, .10x = amount of salt in container 1
and .16y = amount of salt in container 2
and .12(220) = 26.4 = amount of salt in the mix

Since there is a total of 220 ml in the mix, we get

1) x + y = 220

The amount of salt in the mix is the sum of the salt in each container. Therefore,

2) .10x + .16y = 26.4

I get 146-2/3 mL of 10% solution and 73-1/3 mL of 16% solution. These answers are uncommon for this type of problem. Do you know the answers?

Answer 2

The sum of the two volumes
a + b = 220ml

using the concentrations(the amount of salt is constant):

(a).1+(b).16=(220).12

Solve the simultaneous equations

44=.6b
b=220/3
a=2(220)/3=440/3

Answer 3

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