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First thing to answer: What are we solving for?
From the last part of the prompt, we can assume we are solving for the proportion of red bean ice cream cones sold, versus the total number of ice cream cones.

Second thing: What are the knowns, and the unknowns?

We know how many durian ice-cream sales were completed, and how many red bean ice-cream cups were sold.
The only unknown we have here is the number of red bean ice-cream cones sold. However, this has the side effect of leaving the total number of ice-cream sales completed unknown.

How might we calculate the total number of red-bean ice cream cones sold?
We're given a relation between the total number of red bean ice cream sales completed, and the number of red bean ice cream cones. We're also given a relationship between this and the total number of red bean ice-cream cups sold, which we're also given an exact number for. Source:
"The remaining 24 red bean ice-cream were sold in cups."

Our ratio here is: 1/5 of red bean ice-cream sales in cones, and the remainder (24) in cups.
The remainder after subtracting 1/5 from a whole is 4/5, so we can say that 4/5 of the red-bean ice-cream sales were in cups.
Reducing this to the smallest factor and multiplying to get the value of the whole, we first divide 24 by 4 (the numerator), then multiply by 5 (the denominator).

This leaves us with a total of 30 red-bean ice cream sales.

Now, we multiply the total number of red-bean ice cream sales (30) by the proportion of those sales that are in cones (1/5) to get the number of red-bean ice cream cones sold. (6)

We must return now to the total number of ice cream cones sold, which we can assume to be limited to the information provided. We add the durian ice cream purchases (10) to the number of red-bean ice cream purchases (30) to get the total ice cream purchases (40).

Now, we have our proportion: 6 red bean ice-cream cones :: 40 ice-cream sales.

This may be represented by the fraction, 6/40.

We can also reduce this fraction to 3/20, simply because they are equal quantities. This makes it easier to convert to a percent, as 20 is a factor of 100.

If we want to get a percentage from a fraction, we can use a conversion ratio. In this case, our conversion ratio is \(\frac{100\%}{1}\).

This might look odd, but the term "percent" can be traced back to a definition meaning "out of 100" (from the latin "per centum" [that's latin right?]), so 100% would be equal to 100/100, or 1.
In any case, we can then do some multiplication. \(\frac{3}{20} \times \frac{100\%}{1} = \frac{15\%}{1} = 15\%\)

To expand the multiplication, I first divided the 100% value by the denominator, in order ot figure out the value I multiply the numerator by. 100/20 = 5, so I multiplied the 3 on the top left by 5%.
 

This gives me 15%, which I believe to be the answer.

On a side note, it would be appreciated if you were to post how far you got into the problem before getting stuck next time, so that it might be possible to avoid a massive wall of text. I think that doing so would help both of us :)

I'll assume that b and c are non-zero for the purposes of solving, or the answer might be unobtainable. I also think I need to assume them to be finite.

(a+b)/b = a/b + b/b = 5
b/b = 1
a/b + b/b - b/b = 5 - 1
a/b = 4

First, I split the fraction into 2 parts. It isn't helpful immediately, but was helpful with something else, namely...

Second, I used to identity property of division. Namely, dividing a finite, non-zero quantity by itself will yield 1.
Then, I subtract the second equation from the first. This is a very finicky thing to do, but because I know that the values apply the same in both places, I'm doing it anyways.

I could have also written: \(\frac{a}{b} + \frac{b}{b} = \frac{a}{b} + 1 = 5\), then subtracted 1 from each side to get a/b = 4. Different method, same result.

(b+c)/c = b/c + c/c = 4
c/c = 1
b/c + c/c - c/c = 4 - 1
b/c = 3

The numbers and letters are different here, but the steps from above apply the same here.

(a+c)/c = n = a/c + c/c
c/c = 1

a/c + c/c - c/c = n - 1
a/c = n-1
a/c = a/b * b/c
n-1 = 4 * 3
n-1 = 12
n = 13

The important thing that happened here, is I created a "placeholder" variable I named n. I set it equal to the initial quantity that we were solving for, so as to reduce the number of times I write out (a+c)/c, and to also allow operations related to it easier.
The third part of this might look odd, but I chose not to change n, and leave (n-1) in place. This helps, as I note that a/c = n-1, and also equal to a/b * b/c. The b in the numerator and denominator cancel out, and the remaining values match up, thus n-1 = a/b * b/c. However, we don't have a or c, so we keep a/b and b/c, since we have those values and can then find a/c.

From there, we then find n, and with it, the value it represented, as seen below:

(a+c)/c = n = 13
 

Andrea is 68 inches tall.

Hi, not sure this really breaches any forum rules, but putting the link of the problem in the question as having a link as the only content is not the most accessible way that we might be able to help you. If you wanted to point out that the other question got buried, and didn't get an answer, one option might be to put the link as "previous post: ", and then post the problem again.

Answers posted here would seem notably out of context, and would also require lots of tabbing back and forth, making this content primarily a filler on the forum page, burying other people's questions.

PV ==FV / e^(rt)

PV ==78 / e^(0.056 * 9)

      ==78 / e^(0.504)

     ==78 /  1.6553294....

     == $47.12 - what Lily needs to invest today.

\(f(-4)=\frac{a}{b}*-4=\frac{-4a}{b}\\ \frac{-4a}{b}=\frac{-60}{13}\\ \frac{4a}{b}=\frac{60}{13}\\ \frac{a}{b}=\frac{15}{13}\\ a=\frac{15b}{13}\)

\(f(4)=ab*4^2=16ab\\ 16ab=3120\\ ab=195\\~\\ so\\ \frac{15b}{13}*b=195\\ \frac{b^2}{13}=13\\ b^2=13^2\\ b=\pm13 \)

You can check what I have done and continue from there.

LaTex:

f(-4)=\frac{a}{b}*-4=\frac{-4a}{b}\\
\frac{-4a}{b}=\frac{-60}{13}\\
\frac{4a}{b}=\frac{60}{13}\\
\frac{a}{b}=\frac{15}{13}\\
a=\frac{15b}{13}

Angle ACB = 50 degrees

~~~~~~~~~~~~~~~~~~~~~~

Angle ABC = 40 degrees

(Angle BAC = 90 degrees)

Alex, Justin, and Roy shared a sum of money. Alex received 1/2 of the total share of Justin and Roy. Justin received 1/3 of the total share of Alex and Roy. If Roy received $180 more than Justin, how much was the sum of money they shared?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A + J + R = x

A = x/3

J = x/4

R = x/4 + 180

x = x/3 + x/4 + (x/4 + 180)

x = 1080  

There are 20 integers $i$ that work.

The largest possible expression is $(8 - (-2))^5 = 100000$.

This question has been asked numerous times lately. Go look for an old answer.

Very impressive guest :)

In  triangle ABC, CA=4sqrt(2), CB=4sqrt(7), and A=60 degrees. What is B in degrees?

Hello Guest!

sine law:

\(\frac{sinB}{\overline {CA}}=\frac{sinA}{\overline{CB}}\)

\(\frac{sinB}{4\sqrt{2} }=\frac{sin60°}{4\sqrt{7}}\\ \frac{sinB}{4\sqrt{2} }=\frac{\frac{1}{2}\sqrt{3} }{4\sqrt{7}}\\\)

\(sinB=\dfrac{\frac{1}{2}\sqrt{3}\cdot4\sqrt{2}}{4\sqrt{7}}=\dfrac{1}{2}\sqrt{\frac{6}{7}}\\ \angle B=asin\ (\dfrac{1}{2}\sqrt{\frac{6}{7}})\)

\(\angle B=27.575°\)

  !

790==20/2 * [2*(-8) + 19D], solve for D

D==5 - this is the common difference

20th term ==[- 8 + 5 * (20 - 1) ]

                   ==[- 8 +  (5 * 19) ]

                   ==[ - 8 +   95]

                   == 87 - the 20th term

Your sequence looks like this:

-8 , -3 , 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 , 42 , 47 , 52 , 57 , 62 , 67 , 72 , 77 , 82 , 87 , >>Number of terms = 20>>Total Sum == 790

the answer is-44 because 49+-44=49-44=5

it is -44 because 49+-44=49-44 which equals 5

Angle ABC is 65 degrees.

The constant term is 12.

sorry, it says it's incorrect. @asinus can you help?

What real value of t produces the smallest value of the quadratic t^2 - 9t - 36 + t^2 + 7t - 16?

Hello Guest!

\(f(t)=2t^2 - 2t - 52\\ \frac{df(t)}{dt}=4t-2=0\\ 4t=2\\ \color{blue}t=\frac{1}{2}\)

\(t=\frac{1}{2}\) produces the smallest value of the quadratic t^2 - 9t - 36 + t^2 + 7t - 16.

  !

If you let x go infinity, then you get 0 = A - B.

If you let x = 0, then you get 7/2 = A/(-2) + B.

The solution to this system is then A = 7, B = 7, so (A,B) = (7,7).

2, 2, 5, 5, 9, 9==6 digits ==6!/2!.2!.2!==90 permutations as follows:

[(2, 2, 5, 5, 9, 9), (2, 2, 5, 9, 5, 9), (2, 2, 5, 9, 9, 5), (2, 2, 9, 5, 5, 9), (2, 2, 9, 5, 9, 5), (2, 2, 9, 9, 5, 5), (2, 5, 2, 5, 9, 9), (2, 5, 2, 9, 5, 9), (2, 5, 2, 9, 9, 5), (2, 5, 5, 2, 9, 9), (2, 5, 5, 9, 2, 9), (2, 5, 5, 9, 9, 2), (2, 5, 9, 2, 5, 9), (2, 5, 9, 2, 9, 5), (2, 5, 9, 5, 2, 9), (2, 5, 9, 5, 9, 2), (2, 5, 9, 9, 2, 5), (2, 5, 9, 9, 5, 2), (2, 9, 2, 5, 5, 9), (2, 9, 2, 5, 9, 5), (2, 9, 2, 9, 5, 5), (2, 9, 5, 2, 5, 9), (2, 9, 5, 2, 9, 5), (2, 9, 5, 5, 2, 9), (2, 9, 5, 5, 9, 2), (2, 9, 5, 9, 2, 5), (2, 9, 5, 9, 5, 2), (2, 9, 9, 2, 5, 5), (2, 9, 9, 5, 2, 5), (2, 9, 9, 5, 5, 2), (5, 2, 2, 5, 9, 9), (5, 2, 2, 9, 5, 9), (5, 2, 2, 9, 9, 5), (5, 2, 5, 2, 9, 9), (5, 2, 5, 9, 2, 9), (5, 2, 5, 9, 9, 2), (5, 2, 9, 2, 5, 9), (5, 2, 9, 2, 9, 5), (5, 2, 9, 5, 2, 9), (5, 2, 9, 5, 9, 2), (5, 2, 9, 9, 2, 5), (5, 2, 9, 9, 5, 2), (5, 5, 2, 2, 9, 9), (5, 5, 2, 9, 2, 9), (5, 5, 2, 9, 9, 2), (5, 5, 9, 2, 2, 9), (5, 5, 9, 2, 9, 2), (5, 5, 9, 9, 2, 2), (5, 9, 2, 2, 5, 9), (5, 9, 2, 2, 9, 5), (5, 9, 2, 5, 2, 9), (5, 9, 2, 5, 9, 2), (5, 9, 2, 9, 2, 5), (5, 9, 2, 9, 5, 2), (5, 9, 5, 2, 2, 9), (5, 9, 5, 2, 9, 2), (5, 9, 5, 9, 2, 2), (5, 9, 9, 2, 2, 5), (5, 9, 9, 2, 5, 2), (5, 9, 9, 5, 2, 2), (9, 2, 2, 5, 5, 9), (9, 2, 2, 5, 9, 5), (9, 2, 2, 9, 5, 5), (9, 2, 5, 2, 5, 9), (9, 2, 5, 2, 9, 5), (9, 2, 5, 5, 2, 9), (9, 2, 5, 5, 9, 2), (9, 2, 5, 9, 2, 5), (9, 2, 5, 9, 5, 2), (9, 2, 9, 2, 5, 5), (9, 2, 9, 5, 2, 5), (9, 2, 9, 5, 5, 2), (9, 5, 2, 2, 5, 9), (9, 5, 2, 2, 9, 5), (9, 5, 2, 5, 2, 9), (9, 5, 2, 5, 9, 2), (9, 5, 2, 9, 2, 5), (9, 5, 2, 9, 5, 2), (9, 5, 5, 2, 2, 9), (9, 5, 5, 2, 9, 2), (9, 5, 5, 9, 2, 2), (9, 5, 9, 2, 2, 5), (9, 5, 9, 2, 5, 2), (9, 5, 9, 5, 2, 2), (9, 9, 2, 2, 5, 5), (9, 9, 2, 5, 2, 5), (9, 9, 2, 5, 5, 2), (9, 9, 5, 2, 2, 5), (9, 9, 5, 2, 5, 2), (9, 9, 5, 5, 2, 2)] >Total distinct permutations = 90

20! ==2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 5 , 5 , 5 , 5 , 7 , 7 , 11 , 13 , 17 , 19 , Total Prime Factors = 36
Distinct Number of Factors = 8

18! ==2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 5 , 5 , 5 , 7 , 7 , 11 , 13 , 17 , Total Prime Factors = 32
Distinct Number of Factors = 7

20! / 18! ==2 , 2 , 5 , 19 , Total Prime Factors = 4
Distinct Number of Factors = 3