Ike, 2.3, Solving a Mixture Problem

Today was relatively brief in its lesson as due to a technical failure (?) of homework from the previous night. We did cover how to SOLVE A MIXTURE PROBLEM!, though, and so I shall review over this amazingly fun and wildly interesting material for you. Yay!

MIXTURE PROBLEM:
James has 20 ounces of a 20% salt solution. How much salt should he add to make it a 25% solution?

Step One: Set up a table for salt.

	original	added	result
concentration
amount

Step Two: Fill in the table with information given in the question.

John has 20 ounces of a 20% of salt solution. How much salt should he add to make it a 25% solution?

The salt added is 100% salt, which is a 1 in decimal form.
Then you can go ahead and change the rest of the percents to decimal form for easier simplifying. I mean, you dont HAVE to, but thats how i know how to do it. Great!

Then let x= amount of salt added. You get 20 +x.

	original	added	result
concentration	0.2	1	0.25
amount	20	x	20 + x

Step 3: Multiply down each column.

	original	added	result
concentration	0.2	1	0.25
amount	20	x	20 + x
multiply	0.2 × 20	1 × x	0.25(20 + x)

Step 4: original + added = result

0.2 × 20 + 1 × x = 0.25(20 + x)
4 + x = 5 + 0.25x

Isolate variable x
x – 0.25x = 5 – 4
0.75x = 1

Answer: He's got to add 4/3 ounces of salt. YAY!

um.. next scribe... amelia? I dont know! aaahhh dont hate me.