# quantitative problems

#### ibo man

##### Senior Member
10+ Year Member
15+ Year Member

A). What is the probability of six tails out of nine tosses of a fair coin? The answer is 21/128. Please explain.

B). A donut shop bakes a dozen donuts at a cost of \$4. To achieve a 33% profit on sales, what is the minimum sale price the donut shop should set each donut? The answer is 50 cents.

C). A candy store mixes jaw breakers worth 36 cents a pound with lolly pops worth 52 cents a pound to make a 200 pound mixture worth 40 cents a pound. How may pounds of lolly pop did the store use? The answer is 50 pounds.

I would appreciate it if you could explain the answers to me. Thanks.

#### portlander

##### Member
7+ Year Member
15+ Year Member
For the 6 tosses out of 9 question:

This one involves a permutation. What you do is use the formula "n things taken p at a time"

n!/p! (n-p)!

Use this equation where 9 is n and 6 is p:

You get: 9!/6!(9-6)! = 9!/6!(3)! = (9x8x7)/(3x2x1) (cancel out the 6 factorial by extending the 9 factorial)

This equals 84. This number is the number of possible ways this event can happen.

THEN, you use the formula 1/2 x 1/2 x 1/2 etc... to calculate the denominator....this number is equal to the number of possible outcomes of each toss.

So then you have 84/512 wish amazingly reduces to 21/128.

The easier way to reduce this, which is hard to show on the computer is to write out in the denominator "2x2x2x2x2x2x2x2x2"
and cancel the factors of 2 in the nominator.

Did this make any sense? Memorize the permutation equation. It works for figuring out how many ways you can organize X number of people in a line, etc...

#### UBTom

##### Class '04 official geezer
10+ Year Member
15+ Year Member
Question B is easy too.

33% is roughly 1/3. So the question is what sum do you sell 12 donuts for in order to keep 1/3 of the sale money as profit?

So if you sell the 12 donuts for \$6, you keep \$2 (which is 1/3, or 33.3333333% of \$6) as profit after taking away \$4 for the cost of making them. And \$6 divided by 12 is 50 cents per donut.

[Homer] Mmmm.... Donut.... [/Homer] Heh heh..

HTH!

#### mzalendo

##### Member
15+ Year Member
let the no of jaw breakers be X and the No of lol be y

x+Y=200
(.36x+.52y)/(x+Y)=40
(.36x+.52y)/200=40
.36x+.52y=.4(200)
.36x+(200-x).52=80
.36x+104-.52x=80
.16x=24
x=150
Given that x+y=200
y=50 answer(No of Lollipops) I hope these are blue coz my favorite color is blue.

#### ibo man

##### Senior Member
10+ Year Member
15+ Year Member
portlander, UBTom, mzalendo,
Thank you guys very much. You guys are the greatest. I know I can count on you people. Thanks

#### mzalendo

##### Member
15+ Year Member
mzalendo has one more thing to say about question 2
the answer to this problem actually depend on the choices provided. Provided it is a number above 44.33 cents ~.45 centsthis is why
12 donuts =400 cents
1 donut =1/12*400cents
=33.33 cents or like portlander suggested
33(1/3)cents
100%=100/3
133%=(133/100)(100/3)
=133/3
=44(1/3)
confirmation pick any number above 44.33 say 45 cents 12 donuts will cost 5.4 dollars the percentage profit is
140/400x100=35 %
any number in the choices above 44.33 even 44.35 cents should work.
I hope these are choclate glazed donuts coz I love them

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