8.2 Mixtures

% Amount

$

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8.2 Mixtures

A mixture is a combination of different things put in the same container. They can be liquids (a blend of orange juice and apple juice) or they can be solids (different colored jelly beans in the same bowl).

This topic teaches you how to find a missing amount, percentage, or price of an object when given information about the mixture. This topic is very usable in real life.

8.2 Mixtures

Your teacher used to be a firefighter. Before he was hired full time, he had to volunteer. He was hired on full time because he could do things with math that other people couldn’t do. Math got him hired!

Here’s how it happened...

…and it was easy!

8.2 Mixtures

There are times when a firefighter needs to start a fire to fight a fire. They will use a fusee or a drip torch.

Fusee Drip Torch

8.2 Mixtures

A drip torch takes a special mixture of oil and gas. Your teacher had to mix different combinations of gasoline and oil to come up with the correct Drip Torch percent.

Since no one else could do what you are going to learn in this lesson, I got a job!

You never know when your math skills will get you noticed.

Go Math.

8.2 Mixtures

Solve the Problem:

Scott needs 20 gallons of a 15% mixture of oil to gas for his drip torch. He has some mixture at 10% and some mixture at 25%. How much of the 10% solution and the 25% solution do you need to make your drip torch oil?

The problem is asking me to find two different things…Gallons of oil/gas at 10%Gallons of oil/gas at 25%

When the mixture is combined, we should get 20 gallons of a 15% solution.

8.2 MixturesScott needs 20 gallons of a 15% mixture of oil to gas for his drip torch. He has some mixture at 10% and some mixture at 25%. How much of the 10% solution and the 25% solution do you need to make your drip torch oil?

To solve, we start with a 3 x 3 table…

Please draw this table with all the notations.

Amt % or $ TTL

+=

Read the problem and circle the amounts and percentages.

Place the amt and % in the right column.20 15

2510

Big Hint: The words “create”, “make”, “needs”, etc. indicate a bottom row item.

8.2 Mixtures

We need to fill in the two boxes in the Amt column.

Amt % or $ TTL

+=

20 15

2510

One of them we call “x”…

X

The other is called“20 - x”…

20 - X

The second box is tricky! Please remember the pattern is “-”.

8.2 Mixtures

The answer to Scott’s problem of mixing oil and gas to get the correct percentage is…

Amt % or $ TTL

20 15

251013.3

6.7

133167

300

8.2 Mixtures

Multiply Each Row

Amt % or $ TTL

+=

20 15

2510

Now we create an equation…and solve.

X20 - X

10x25(20-x)

20*15

10x + 25(20-x) = 20*15

10x + 500 – 25x = 300

– 15x = - 200 x = 13.3

+=

20-x = 20 – 13.3 = 6.7

8.2 Mixtures

This topic requires lots of practice to get good at it. Let’s try some more. Be sure to start with a grid, circle your math terms, and place your amounts and percentages in the right boxes. When satisfied, create an equation and solve…

Big Hint: They won’t tell you in the paragraph, items like water and skim milk are “0%” and items like pure copper, pure iron, and pure most anything else is “100%”.

For example, if the paragraph says orange juice or apple juice, they mean 100% juice.

8.2 Mixtures

Ex 2: How many gal. of a 80% saline solution must be mixed with 3 gal. of a 20% saline solution to make a 68% solution?Make a Grid Amt % or $ TTL

+=

Circle Terms

“make” is bottom row

68Fill in the rest

80

3 20

x

Unknowns?

x + 3

Make equation… 80x + 3*20 = 68(x + 3)

Now solve… Answer: 12 gal.

8.2 Mixtures

Ex 3: 3 kg of arugula were mixed with 1 kg of spinach which costs $2/kg to make premium salad mix which costs $5/kg. What is the price per kg of arugula?

Now do it yourself without help.Click through for each step.

Amt % or $ TTL

5

x

1 2

3

4

3x + 1*2 = 4*5

Answer: $6.00