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## Comment on

Mixture Questions## Hello Brent,

Could you please explain this question?

A mixture of 12 ounces of vinegar and oil is 40%n vinegar by weight. How many ounces of oil must be added to the mixture to produce a new mixture that is only 25% vinegar? Also is there an easier and faster approach than sketching the figures of solutions? There are many in other sources, but I do not want to confuse. I want a method from you.

## INITIAL mixture: 12 ounces,

INITIAL mixture: 12 ounces, which is 40% vinegar

40% of 12 = 4.8

So, the INITIAL mixture contains 4.8 ounces of vinegar

Let x = number of ounces of oil that we must ADD to the initial mixture.

IMPORTANT: Once we add x ounces of oil to the initial mixture, the RESULTING mixture will have a total volume of 12+x ounces

Also, the RESULTING mixture will contain 4.8 ounces of vinegar

GOAL: We want the resulting mixture to be 25% vinegar.

In other words, we want the resulting mixture to be 1/4 vinegar

So, we get: 4.8/(x+12) = 1/4

Cross multiply to get: (1)(x+12) = (4)(4.8)

Expand and simplify: x + 12 = 19.2

Solve: x = 7.2

So, we must add 7.2 ounces of oil

## Hello Sir,

For a mixture problem, what I normally do is, draw 3 boxes, and try to set up an algebraic equation.

for this problem, my equation was,

.40(12) + x = .25(12 + x)

but I see the, the correct equation is, .40(12) = .25(12 + x)

I don't know why, why the [ +x ] portion from the left side of the equation i wrote wasn't included into the equation.

is it because, the question is asking for a final mixture that is "only vinegar" instead of the phrase "resulting solution", that we normally see on other questions!

eagerly waiting for your reply.

Thanks :)

## Notice that (0.40)(12)

Notice that (0.40)(12) represents the volume of VINEGAR in the initial mixture.

Likewise, (0.25)(12 + x) represents the volume of VINEGAR in the resulting mixture.

So, our equation is keeping track of the volume of VINEGAR throughout the process.

In the equation, x = number of ounces of OIL that we must add to the initial mixture.

Since there's no vinegar in the oil, we don't add x.

Alternatively, we COULD say that the oil we're adding is 0% vinegar.

So, we could write: 0.40(12) + (0.0)(x) = 0.25(12 + x)

Does that help?

## 100 percent clear Sir,

Thank you so much, you’re amazing :)

## It is helpful

## Thank you! The catch in this

## Another way to approach this

300(30%) + 200(70%) = 500(c) --> 300 * .3 + 200 * .7 = 500*c

90 + 140 =230 = 500 * c

c = (230/500) *100 = 46%

## Perfect!

Perfect!

## A cup full of water when

grape solution.

Column A : volume of the cup

Column B: 400 cc

sir how to solve this question?

## ASIDE: I'll use milliliters

ASIDE: I'll use milliliters (ml) instead of cubic centimeters (cc)

Start with 100 ml of 30% grape solution.

So, this initial solution contains 30 ml of grape solution, and 70 ml of water.

Now add x ml of pure water (i.e., x = the volume of the cup).

So, this part contains 0 ml of grape solution, and x ml of water.

When we combine the two amounts we get: 30 ml of grape solution and (70 + x) mls of water.

Also, note that the TOTAL volume of the resulting solution = (100 + x) mls

We want the resulting solution to be 10% grape solution.

In other words, we want: (volume of grape solution in resulting solution)/(TOTAL volume of resulting solution) = 10%

In other words: (30)/(100 + x) = 10/100

Simplify: (30)/(100 + x) = 1/10

Cross multiply to get: (1)(100 + x) = (30)(10)

Expand: 100 + x = 300

Solve: x = 200

So, the volume of the cup = 200 ml

We get:

QUANTITY A: 200

QUANTITY B: 400

Answer: B

Cheers,

Brent

## During a college fun-fair,

Pls solve

## Yikes! That's a poorly-worded

Yikes! That's a poorly-worded question!

The addition of "(and their family members)" makes this question unanswerable.

However, if we IGNORE that proviso, and assume that all 75 attendees are either students or teachers, (no family members), then we can answer the question as follows:

Let t = # of teachers who went

Let x = # of students who went

So, we can write:

t + x = 75

30t + 12x = 1800

When we solve the system, we get: t = 50 and x = 25

Answer: 25 students.

Cheers,

Brent

## I got the same answer but

## https://greprepclub.com/forum

Can you provide an explanation to the question posted above, I'm not quite understanding how the answer came to be.

Thank you!

## Here's my full solution:

Here's my full solution: https://greprepclub.com/forum/a-makes-up-8-percent-of-solution-r-and-18-...

Cheers,

Brent

## https://greprepclub.com/forum

When 6l pure acid is added isnt the resulting mixture total 26? since there is 8l of some other liquid?

## Question link: https:/

Question link: https://greprepclub.com/forum/a-container-holds-10-liters-of-a-solution-...

We start with 10 liters of ORIGINAL solution

Although this original solution consists of 2 liters of acid and 8 liters of some other liquid, the TOTAL volume is 10 liters.

So, if we add 6 more liters to the ORIGINAL 10 liters, the resulting volume = 10 + 6 = 16

Does that help?

Cheers,

Brent

## This technique took some

## Thanks, Kevin!!!

Thanks, Kevin!!!

## Hello Sir,

Is there an algebraic solution to this question, I couldn't solve it the way I normally do, like drawing boxes and breaking it into parts!

"Suppose you have a 200-liter mixture that is 90% water and 10% bleach and ask how much water you would need to add to make it 5% bleach"

Thanks

## We start with 200 liters of

We start with 200 liters of solution

10% of 200 = 20

So, the original solution contains 20 liters of bleach

Let x = the volume of water (in liters) we must add to get a solution that is 5% bleach

This means the NEW volume of the solution = 200 + x

The volume of bleach is still 20 liters (since we didn't add any bleach the original solution)

We want the new solution to be 5% bleach.

In other words, we want: (volume of bleach)/(volume of solution) = 5/100 (aka 5%)

Substitute to get: 20/(200 + x) = 5/100

Simplify to get: 20/(200 + x) = 1/20

Cross multiply: (1)(200 + x) = (20)(20)

Expand: 200 + x = 400

Solve: x = 200

So we must add 200 liters of water.

## Got it, Sir, Thank you so

## How many liters of 20%

## Here's my full solution:

Here's my full solution: https://greprepclub.com/forum/topic20540.html#p60664