Let's work through this problem step by step, using a chart to help us organize our information. Click through the steps in the slideshow, and then try answering the question at the bottom of the page.
You have two sodium solutions in two different containers. The first solution consists of 25 percent sodium and 75 percent water, while the second solution consists of 2 percent sodium and 98 percent water.
How many mL of each solution do you need to make 100 mL of an 18 percent sodium mixture?
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Define the Known and the Unknown We know we have two different containers, each with a certain percentage of sodium. We are trying to figure out how many mL from each container will make up the 100 mL total. So let x = # of mL in container one and y = # of mL in container two. Get Organized At this point, it is often helpful to create a table to organize your information. In the table below, notice the row and column labels so that each element is quickly identified. The # of mL of sodium is calculated by multiplying the # of mL by the percentage of sodium.
Write Your Equations Using the table, we have two equations. Solve the System Solve the first equation for x: x = 100 − y Now, substitute into the second equation.
Answer the Question 30.43 mL from container one and 69.57 mL from container two make up 100 mL of the mixture. |
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Question
Can you think of a different way to solve this problem?
.75x + .98y = .82(100)
This would have given us the same answer. You could also try using the seesaw equation. Two percent is 16 away from 18 percent and 25 percent is 7 away from 18 percent.
16(100 - x) = 7x
1600 - 16x = 7x
1600 = 23x
69.57 = x
