Mixture problems: shampoo mix; potpourri; yarn mix; juice

[ysodimu]

Please help with the questions below, if I get the equation or what the equation should be I can solve or try solving. I really need help, I am very very bad in Math especiallay any kind of Word Problems: Thanks in advance.

Q1: A hair stylist combines 12 oz of shampoo that is 20% conditioner with an 8 ounce bottle of pure shampoo. what is the percent concentration of conditioner in the 20 ounce mixture.

Q2: to make the potpourri mixture sold at a florist shop, 70 ox of a potpourri that is 80% lavender are combined with a potpourri that is 60% lavender. The resulting potpourri is 74% lavender. How many of the potpourri that is 60% lavender is used?

Q3: A rug is made by weaving 20 lb of yarn that is 50% wool with a yarn that is 25% wool. How many pounds of the yarn that is 25% wool must be used if the finished rug is to be 35% wool?

Q4: A caterer made an ice cream punch by combining fruit juice tha tcosts $4.50 per gallon with ice cream that costs $6.50 per gallon. How many gallons of each were used to make 100 gal of punch cosing $5 per gallon?

 

[Denis]

Re: Mixed problems

Q1: A hair stylist combines 12 oz of shampoo that is 20% conditioner with an 8 ounce bottle of pure shampoo. what is the percent concentration of conditioner in the 20 ounce mixture.

Those are all basically done like this:
a @ x
b @ y
======
a+b @ z

z = (ax + by) / (a + b)

With Q1 :
12 @ 20
8 @ 100
======
20 @ z
z = (12 * 20 + 8 * 100) / (20) = 52

Depending on the "givens", you could have to solve
for any of a,b,x,y,z.

 

[Loren]

Q1: A hair stylist combines 12 oz of shampoo that is 20% conditioner with an 8 ounce bottle of pure shampoo. what is the percent concentration of conditioner in the 20 ounce mixture.

This is called a "mixture" problem. Most mixture problems can be solved by selecting one of the components of the mixture and building an equation that the amount of that component in one container plus the amount of that same component in a second container equals the amount of that component in the final mixture of the two liquids. In this case, we can select "conditioner" as the component. We have two containers, one that is 12 oz. containing 20% conditioner. The second bottle is 8 oz of 100% shampoo. That means there is 0% conditioner in the second bottle. We pour these two bottles into a third container and wonder what percent is conditioner.

Amount ofconditioner in first container is .20(12) oz.
Amount of conditioner in second container is 0 oz.
The amount of conditioner in the third container will be x(20) oz.

This gives us the equation .2(12) + 0 = 20x.

Solving for x, we get x=.12 which is converted to 12% because they asked "what percent".

You could have set up and equation using amount of shampoo. It would look like this.

.80(12) + 1.00(8) = 20y (where y represents percent of shampoo.

Solving for y we get 88% shampoo. Therefore the the rest, 12% must be conditioner.

I urge you to think this through thoroughly an carefully and then apply to your other problems.

 

[stapel]

Please help with the questions below, if I get the equation or what the equation should be I can solve or try solving.

The solving is the easy part. The translation of the English into math, and the set-up of the equations is what you need to learn. :!:

You keep posting more of the exact-same sort of exercise, which suggest that you might need to do some studying. If the hints and suggestions you've been given are still leaving you lost, then you're not ready yet for that, and need to start at the beginning. :idea:

So please consider taking advantage of some of the many great lessons available online:

. . . . .Google results for "mixture word problems"

Once you have studied some lessons (at least two!) and have learned the basic terms and techniques, please attempt these exercises. If you get stuck or are unsure of your solutions, please reply showing all of your work and reasoning so far. Thank you!

Eliz.