Question

A pharmacist wants to mix a 16% saline solution with a 44% saline solution to get 28 L of a 36% saline solution. How much of each solution should she use?

19 L of the 16% solution; 9 L of the 44% solution

9 L of the 16% solution; 19 L of the 44% solution

8 L of the 16% solution; 20 L of the 44% solution

20 L of the 16% solution; 8 L of the 44% solution

Answer 1

You need a table to solve this problem. It will consist of 3 rows and 3 columns. The column across the top will be "number of liters", second column will be "% saline", and third column will be "total". First row will be 16% saline, second row will be 44% saline, and third row will be the "mix", the sum of the 2 strengths of solution. In the first row first column we will put x, since we don't know how much 16% saline we have. First row second column we will put .16, since that is the decimal equivalent to 16%, and in the total column we will put the product of x and .16 which is .16x. Second row first column we put a y since we don't know how much 44% saline solution we have. Second row second column we have .44 since that is the decimal equivalent to 44%, and the third column is the product of those 2 which is .44y. In the "mix" row, we have 28 in the first column since we want 28 L of the new solution, and in the second column we have .36 since we want this new solution to be 36% saline. The product of those 2 will go into the third column. That number is 10.08. The first column is the number of liters of solution. We know that we are adding the 2 different strength solutions to get a new solution with a new strength, so that equation, going straight down the first column, is x + y = 28. Going straight down the third column, we will add the strengths of these solutions. .16x + .44y = 10.08. We solve the first equation for x and get x=28-y. Sub that value into the second equation in place of x to get

.16(28-y) + .44y = 10.08. Distribute through the parenthesis to get 4.48 - .16y + .44y = 10.08. Combine like terms to get .28y = 5.6. Divide by .28 to get that y = 20. That means there are 20 liters of 44% saline in the mixture. If there are a total of 28 liters, then that means that there is 8 liters of 16% saline solution in the mixture.

Answer 2

Answer:

8 L of the 16% solution; 20 L of the 44% solution

Step-by-step explanation:

Let x is the amount of 16% saline and 16% = 0.16

Let y is the amount of 44% saline and 26% = 0.44

Total needed saline = 36% = 0.36

The amount of saline is:

$0.16x+ 0.44y=0.36(28)$     ....(1)

Total amount needed is 28L so, equation becomes:

$x+y=28$    ....(2)

Substituting the value of x=28-y in (1)

$0.16(28-y)+0.44y=10.08$

$4.48-0.16y+0.44y=10.08$

$0.28y=5.6$

y = 20

And we know$x+y=28$

So, $x+20=28$

$x=28-20$

x = 8

We can see that 8 L of the 16% solution and 20 L of the 44% solution is needed.