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**Grade 10 Mixture Problems**

A simple presentation by Mr. Agostini

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The Problem A chemistry teacher needs to make 20 L of 40% sulfuric acid solution. The two containers of acid solutions available contain 30% sulfuric acid and 50% sulfuric acid. How many litres of each solution must be mixed to make a container with 40% sulfuric acid solution.

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The Idea Did you know: 30% sulfuric acid contain is made up of 30% acid and the rest is water to dilute the solution. So in a 100 L container, 30L is acid and 70 L is water. You are going to mix the containers together to obtain 20 litres of a solution that 40% of it will be sulfuric acid. How many litres from each container will we need to use to make this mixture. If you had to guess, what would you say: Recall 30% acid in one container and 50% in the other. You need 40% in the mixture. How many litres from each mixture do you think we would need.

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**Defining your Variables First**

Define your variables first: (Remember the last sentence in the question usually tells us what we are looking for) Let x be the amount in L that is poured from container 1 at 30% acid solution Let y be the amount in L that is poured from container 2 at 50% acid solution

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**Creating your two equations: Equation 1**

Equation 1 is usually build on the amount of liquid (in this case) that is required. We need 20 L. Therefore: x amount is being poured in from container 1 and y amount is being poured in from container 2, to make 20 L. Their sum is 20 then. So the equation is: x + y = 20 (Equ: 1)

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**Creating your two equations: Equation 2**

We create equation 2 from the amount of pure acid that is needed from each container and how much pure acid is in the 20L container. (Recall: 40% of 20 L of pure acid is required) The amount(L) of pure acid from container 1 will be 30% of x amount(L) poured into the beaker or 0.30x. The amount(L) of pure acid from container 2 will be 50% of y amount(L) poured into the beaker or 0.50y Therefore, we combine 30% of x with 50% of y to obtain 40% of 20 L The second equation is: 0.30x y = 0.40(20) (Equ: 2)

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**So what do we have: Let x = amount in L of 30% sulphuric acid soluton.**

Let y = amount in L of 50% sulphuric acid soluton. (1) x + y = 20 (2) 0.30x y = 0.40(20) Or (2) 0.3x + 0.5y = 8

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**When Solving you can use any method you wish. Yay!!!!!**

Elimination Method: ( x -3) ( x 10) -3x – 3y = -60 3x + 5y = 80 Back sub into x + y = 20 x + 10 = 20 x = 20 – 10 x = 10 Therefore 10 L of container 1 (at 30% acid solution) and 10 L of container 2 (at 50% acid solution) is needed to make 20 L at 40% acid solution. x + y = 20 0.3x + 0.5y = 8 + 2y = 20 y = 10

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**When Solving you can use any method you wish. Yay!!!!!**

Substitution Method: (1) x + y = 20 Back sub into x + y = 20 (2) 0.3x + 0.5y = 8 10 + y = 20 y = 20 – x sub into (2) y = 0.3x + 0.5(20 – x) = 8 y = 10 0.3x + 10 – 0.5x = 8 Therefore 10 L of container 1 (at 30% acid solution) and 10 L of container 2 (at 50% acid solution) is needed to make 20 L at 40% acid solution. 0.3x – 0.5x = – 0.2x = - 2 x = 10

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