algebra - Can you please explain to me mixture problems like the following: Annabel has 25 ounces of a 20% boric acid solution which she wishes to dilute to a 10% solution. How much water does she need to add in order to obtain the 10% solution?

Can you please explain to me mixture problems like the following: Annabel has 25 ounces of a 20% boric acid solution which she wishes to dilute to a 10% solution. How much water does she need to add in order to obtain the 10% solution?

215 viewed last edited 3 years ago

algebra explain

EngagingKangaroo (Minor, 5^th Grade)

Mahesh Godavarti (last edited 4 years ago) (Expert, Founder @Qalaxia)

There are several types of problems of this kind:

However, to solve all problems of this kind, we first need to understand what concentration is = \frac{volume\ of\ solute}{total\ volume=volume\ of\ solute+volume\ of\ solvent} or it's simply the ratio of the volume of the solute to the total volume of the solution.

Therefore, we can restate the problem in terms of ratio.

Annabel has 25 ounces of a boric acid solution where the ratio of the volume of the boric acid to the total volume is 1/5. She wants to make the ratio of the volume of the boric acid to the total volume to be 1/10. How much water does she needs to add?

This is a linear equation in one variable. Let x be the number of ounces she needs to add. Let's calculate the starting volume of boric acid and water, since the ratio of boric acid to total is 1/5, this means that 1/5 of 25 ounces is boric acid and 4/5 of 25 ounces is water. Therefore, we have 5 ounces of boric acid and 20 ounces of water.

Since, we want the final concentration to be 1/10 or the ratio of volume of the boric acid to total volume is /10, we have 5/(x + 25) = 1/10. Therefore, 50 = x + 25 and x = 25.

If you can do problems of the following kind, you can handle any mixture problems.

The ratio of boys to the total number of students in a class of 25 students is 1/5. How many more girls should be added to the class so that the ratio of boys to the total number of students in the class becomes 1/10.

EngagingKangaroo (last edited 4 years ago) (Minor, 5^th Grade)

PLZ HELP ME!!!!! I NEED HELP WITH THIS THX TO WHOEVER HELPS!!!

Sangeetha Pulapaka (last edited 4 years ago)

Sure E.K. Just give me five minutes. I am typing the solution for you. Are you referring to the mixture word problems in algebra?

Sangeetha Pulapaka (last edited 4 years ago)

WAITING FOR YOUR ANSWER!

Krishna (last edited 3 years ago) (Expert, Educator @Qalaxia)

Mixture is created whenever differing kinds of things are combined to form a 3rd, “mixed” item.

In the mathematics, mixture problems involve creating a mix from two or more things, then determining some quantity (percentage, price, rate, etc) of the resulting mixture.

EXAMPLE: if you combine 10 liters of pure water with 15 liters of a 30% alcohol solution, what's the concentration of the resulting mixture?

EXAMPLE 2: if you combine 10lbs of peanuts costing $1.50 per pound with cashews costing $2.50 per pound, what number pounds of cashews would you would like to add so the resulting mixture includes a cost per pound of $1.95?

https://www.purplemath.com/modules/mixture2.htm

http://www.analyzemath.com/math_problems/mixture_problems.html

Krishna (last edited 4 years ago)

If you want more details or any issue with any problem. share here, I will help you

EngagingKangaroo (last edited 4 years ago)

Ok thank you I will

Mahesh Godavarti (last edited 4 years ago) (Expert, Founder @Qalaxia)

Can you share more information on what you mean by mixture problems?

EngagingKangaroo (last edited 4 years ago)

By mixture problems, I mean problems like Annabel has 25 ounces of a 20% boric acid solution which she wishes to dilute to a 10% solution. How much water does she need to add in order to obtain the 10% solution?

Mahesh Godavarti (last edited 4 years ago)

Okay, will do.

Mahesh Godavarti (last edited 4 years ago) (Expert, Founder @Qalaxia)

Are you something along the lines of https://www.purplemath.com/modules/mixture.htm?