Question

dr. bhatia mixes 2 liters of a 5% saline solution with x liters of a 9% saline solution. the table shows the amount of each solution used. saline solution | amount (liters) | concentration | total
--- | --- | --- | ---
5% saline | 2 | 0.05 | 0.1
9% saline | x | 0.09 | 0.09x
mixture | 2 + x | 0.08 | 0.64
what is the value of x?
options: 6, 5, 4, 3

Explanation:

Step1: Set up the equation from the total saline

The total saline in the mixture is the sum of the saline from each solution. So, \(0.1 + 0.09x = 0.64\).

Step2: Subtract 0.1 from both sides

Subtract 0.1 from each side: \(0.09x = 0.64 - 0.1\). Calculating the right side, we get \(0.09x = 0.54\).

Step3: Solve for x

Divide both sides by 0.09: \(x=\frac{0.54}{0.09}\). Calculating this, we find \(x = 6\). Wait, no, wait, let's check again. Wait, the mixture's total is \(0.08(2 + x)=0.64\). Oh, maybe I made a mistake earlier. Let's use the mixture's concentration. The total saline is also \(0.08(2 + x)\). So the correct equation is \(0.1+0.09x = 0.08(2 + x)\). Let's redo that.

Step1: Correct equation setup

The total saline from 5% solution is \(2\times0.05 = 0.1\), from 9% is \(0.09x\), and from the mixture is \(0.08(2 + x)\). So \(0.1+0.09x=0.08(2 + x)\).

Step2: Expand the right side

\(0.1 + 0.09x=0.16+0.08x\).

Step3: Subtract 0.08x and 0.1

Subtract \(0.08x\) and 0.1 from both sides: \(0.09x - 0.08x=0.16 - 0.1\). So \(0.01x = 0.06\)? Wait, no, that can't be. Wait the table says the mixture's total is 0.64. Wait the table has "Total" as 0.1 for 5% (2*0.05=0.1), 0.09x for 9%, and 0.64 for the mixture. So the total saline in the mixture is 0.64, which is the sum of 0.1 and 0.09x. So \(0.1 + 0.09x = 0.64\). Then \(0.09x=0.64 - 0.1=0.54\), so \(x = 0.54/0.09 = 6\). But the options have 6 as a choice. Wait the options are 6,5,4,3. So x=6? Wait but let's check with the mixture amount. The mixture amount is 2 + x liters, and the total saline is 0.64, so concentration is 0.64/(2 + x)=0.08. So 2 + x=0.64/0.08=8, so 2 + x=8, so x=6. Yes, that's correct. So x=6.

Answer:

6