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
9% saline	x	0.09	0.09x
mixture	2 + x	0.08	0.64

what is the value of x?
○ 3
○ 4
○ 5
○ 6

Explanation:

Step1: Set up the equation for total salt

The total salt from the two solutions should equal the salt in the mixture. So, \(0.1 + 0.09x = 0.64\).

Step2: Subtract 0.1 from both sides

\(0.09x = 0.64 - 0.1\)
\(0.09x = 0.54\).

Step3: Solve for x

Divide both sides by 0.09: \(x=\frac{0.54}{0.09}\)
\(x = 6\). Wait, no, wait, let's check again. Wait, the mixture's total is 0.64? Wait, no, maybe I misread. Wait, the mixture's amount is \(2 + x\) liters, concentration 0.08, so total salt is \(0.08(2 + x)\). So the correct equation is \(0.1 + 0.09x = 0.08(2 + x)\). Let's redo that.

Step1: Correct equation

\(0.1 + 0.09x = 0.08(2 + x)\).

Step2: Expand the right side

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

Step3: Subtract 0.08x and 0.1 from both sides

\(0.09x - 0.08x = 0.16 - 0.1\)
\(0.01x = 0.06\).

Step4: Solve for x

\(x=\frac{0.06}{0.01}=6\)? Wait, but the options include 6? Wait, the options are 3,4,5,6. Wait, maybe my first equation was wrong. Wait, let's check the table again. The 5% solution: amount 2, concentration 0.05, total 20.05=0.1 (correct). 9% solution: amount x, concentration 0.09, total 0.09x (correct). Mixture: amount 2 + x, concentration 0.08, total 0.08(2 + x) = 0.64? Wait, 0.08(2 + x)=0.64? Then 2 + x = 0.64 / 0.08 = 8, so 2 + x = 8, so x = 6. Oh, right! I misread the mixture's total. The mixture's total is 0.64, so 0.08(2 + x)=0.64. So 2 + x = 0.64 / 0.08 = 8, so x = 8 - 2 = 6. Wait, but let's check with the salt. 0.1 (from 5%) + 0.096 = 0.1 + 0.54 = 0.64, which matches the mixture's total. So x is 6. Wait, but the options have 6 as an option. Wait, but let's check again. Wait, maybe I made a mistake earlier. Let's do it with the mixture's amount. If mixture is 2 + x liters, concentration 0.08, total salt 0.08*(2 + x). We know total salt is also 0.1 + 0.09x. So:

\(0.1 + 0.09x = 0.08(2 + x)\)

Wait, no, the table says the mixture's total is 0.64. So 0.08*(2 + x) = 0.64. So 2 + x = 0.64 / 0.08 = 8. So x = 8 - 2 = 6. Yes, that's correct. So x is 6.

Answer:

6 (corresponding to the option with 6, e.g., if the options are A.3, B.4, C.5, D.6, then D.6)