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Grade 10 Mixture Problems. A simple presentation by Mr. Agostini. The Problem.

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### Grade 10 Mixture Problems

A simple presentation by Mr. Agostini

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.

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.

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

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)

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 + 0.50y = 0.40(20) (Equ: 2)

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 + 0.50y = 0.40(20)
- Or
- (2) 0.3x + 0.5y = 8

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

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 = 20 - 10

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 = 8 - 10

– 0.2x = - 2

x = 10

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