Question

You poured some 6% alcohol solution and some 8% alcohol solution into a mixing container. Now you have 600 grams of 7.4% alcohol solution. Write and solve a system of equations to find how many grams of 6% solution and how many grams of 8% solution you poured into the mixing container.

You mixed ___ grams of 6% solution with ____grams of 8% solution.

Answer 1

Answer: 180 grams of 6% solution with 420 grams of 8% solution.

Explanation:

Let x and y be the weight (in grams) of 6% and 8% alcohol solution. Since the total weight is 600 grams, therefore,

`$$\Rightarrow x+y=600 \ldots \text { (1) }`

Using the statement given, we can write the following equation:

`\Rightarrow 6 x+8 y=(7.4)(600)\\ \Rightarrow 6 x+8 y=4440 \text {... (2) }`

Substitute the value of y from equation (1) into equation (2), we'll get:

`\begin{gathered}\Rightarrow 6 x+8(600-x)=4440 \\\Rightarrow 6 x+4800-8 x=4440 \\\Rightarrow 2 x=360 \\\Rightarrow x=180\end{gathered}`

Therefore,

`\Rightarrow y=600-180=420`

Therefore, you mixed 180 grams of 6% solution with 420 grams of 8% solution.

Answer 2

• 180 grams of 6%
• 420 grams of 8%

Explanation:

Let s and e represent the grams of 6% and 8% solution, respectively. The given relations can be described by ...

s + e = 600 . . . . . you have 600 grams of mixture

0.06s +0.08e = 0.074(600) . . . . grams of alcohol in the mixture

__

The first equation can give an expression for s that substitutes nicely into the second equation:

s = 600 -e

0.06(600 -e) +0.08e = 0.074(600) . . . . substitute for s

0.02e = 0.014(600) . . . . . . subtract 0.06(600)

e = 420 . . . . . . . divide by 0.02

s = 600 -420 = 180

You mixed 180 grams of 6% solution with 420 grams of 8% solution.