catmg

Oh, dw about it. 

Do you understand the logic behind the explanation?

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Hello Guest!

I'm a bit confused with part of your question, "If she sells them at 50 dollars a bouquet, she makes a 10 dollar profit for each sale." Was 10 a mistypo of 1? I'm going to assume that it was a typo since I can't figure out what if would mean otherwise. 

Variables

First, let's set x as the number of dollars she raises above $50. 

That would mean that she sells each bouquet at 50 + x, meaning that her profit would be 50 + x - 49 = 1 + x. 

It would also mean that the number of bouquets she's able to sell is 500 - 10x. 

Then, the profit in total is (500 - 10x)(1 + x)

Equation

The goal is to find the value of x that creates the largest answer in this equation, (500 - 10x)(1 + x). 

You could simply graph it out, or you can start simplifying. 

(10)(50 - x)(1 + x)

We want to make it so that (50 - x) is as close to (1 + x) as possible. 

50 - x = 1 + x

51 = 2x

25.5 = x

Answer

Since we're looking for her selling price (50 + x). 

We just need to plug x in. 

50 + 25.5 = 75.5

I hope this helped. :)))))

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Hi Guest!

Sadly, I wasn't able to answer your problem, however I was able to run a quick code in Python that gave me the answer. 

https://repl.it/join/tghttcsn-160782

The total number of possible combinations are 6891. 

6891/117649 is our answer. 

However, I'm not the most sure. 

Sorry I wasn't able to help more.

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Hi Wolfie,

I think you may have answered the wrong problem. In 2019 State Sprint Round, there is a problem like this "Eliza creates a custom 6-sided die by randomly choosing six distinct integers from 1 to 7, inclusive, to paint onto the sides of a blank cube. She tells Philip that the faces of her die have a sum of 24. Philip rolls the die. What is the probability that Philip’s die shows a prime number on the top face? Express your answer as a common fraction."

However, this seems to be a different version of the problem since the numbers don't have to be distinct. 

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I hope everyone has a fantastic 2021. :))))

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Hello Melody, 

Here's the answer explained by AoPS. 

https://artofproblemsolving.com/wiki/index.php/2014_AMC_12A_Problems/Problem_25

It seems like the answer is 40. 

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Hi Wolfie,

I think you may have messed up some of the numbers. 

Woah, you stayed up quite late. 

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Hi Guest!

The x-intercept is 8, and the y-intercept is -10/3. 

I think Wolfie accidentally by 60 instead of 40 when finding them. 

x-intercept

x-intercept is when y = 0. 

5x - 12(0) = 40

5x = 40

x = 8

y-intercept

The y-intercept is when x = 0. 

5(0) - 12x = 40

-12x = 40

x = -40/12

x = -10/3

Distance

We can simply use a^2 + b^2 = c^2 since the x and y intercept form a right angle triangle. 

(-10/3)^2 + 8^2 = 676/9

sqrt(676/9) = 26/3. 

Answer

26/3

I hope this helped.  :)))))

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Hello Guest!

Let's start by setting the measure of angle A as x. 

That would make angle C 5x, and since angle B is congruent to angle C, angle B is 5x too.

Angle A = x

Angle B = 5x

Angle C = 5x

The sum of the angles in a triangle is 180. 

So Angle A + Angle B + Angle C = 180.

x + 5x + 5x = 180

11x = 180

x = 180/11

Since we're looking for Angle B, we just do 180/11*5 = 900/11

I hope this helped :))))

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That's amazing. :)))

I love the feeling of finally understanding a problem. 

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