Melody

Thanks Alan,

Yes L has to be a multiple of 10 but I don't know about his part of a sandwich bit. 

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The reason Liverworst has to be a multiple of 10 is this.

cavier sandwiches are $5 and Bolgna sandwiches are $2.  No matter how many of the these sandwiches you buy it is going ot cost a whole number of dollars.

Altogether the sandwiches cost $100 therefore the liverworst sandwiches must cost a whole number of dollars as well. Since they are 10cents each there must be a multiple of 10 of them.

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Now, there are 100 sandwiches costing $100 altogether so it stands to reason there will be a lot more of the cheap liverworst ones.

I'm going to do it by emimination.

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##Say there are 90 liverworst costing $9 then there can be only 10 more sandwiches. the maximum cost of 10 sandwiches is 10*$5=$50 and that is not enough - they need to cost $100-9=$91

##Say there are 80 liverworst costing $8 then there can be only 20 more sandwiches. the maximum cost of 20 sandwiches is 20*$5=$100 umm lets look more.  

Can C+B=20 ==> 2C+2B=40 (1) and 5C+2B=92?   (2)

(2)-(1)   3C=52     52 is not a multiple of 3 so this doesn't work - C must be a whole number.

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##Say there are 70 liverworst costing $7 then there can be only 30 more sandwiches. Lets look at the equations.

Can C+B=30 ==> 2C+2B=60 (1) and 5C+2B=93?   (2)

(2)-(1)   3C=33     33 is a multiple of 3 so this looks promising  33/3=11cavier sandwiches.

If this is right then there are 70liverworst, 11 cavier, and 19 bologna sandwiches.

70+11+19=100 so far so good!

5C+2B+0.1L=55+38+7=100 great.

There is the answer!   70liverworst, 11 cavier, and 19 bologna sandwiches.

I didn't check if it is the only answer but I expect that it is. It is an answer that fits the data anyway!

Calculus is a huge and very powerful branch of mathematics.

To ask how do i solve calculus is to ask how do i solve algebra.

The question makes no sense!

owen made 100 sandwiches which she sold for exactly $100.

She sold caviar sandwiches for $5.00 each,

the bologna sandwiches for $2.00, and the liverwurst sandwiches for 10 cents.

How many of each type of sandwich did she make?

5C+2B+0.10L=100 => 50C+20B+L=1000 (1)

C+B+L=100 (2)

These are simultaneous equations and nomally they could not be done because there are 3 unknows so you need 3 equations.  This is a little different because C, B and L must be whole numbers.

This means that this is a LINEAR DIOPHANTINE EQUATION.

(1)-(2) = 49C+19B=900

 Maybe you can solve this with trial and error???

To solve it properly I will have to do some serious homework.  (Which given enough time I will do)

step1:  subtract 1.6x from both sides

step2: subtract 5.4 from both sides.

step 3: decide what you need to divide (both sides) by to get rid of the number in front of the x

Try it yourself.

Start by multiplying both sides by 4

I just did it and deleted it accidently.  start by multiplying both sides by 5.  That will get rid of all the fractions.

You try it and see how you go.  

$$\begin{array}{rll}
-3(x-1)&=&9\\
(x-1)&=&-3\qquad \mbox{divide both sides by minus 3}\\
x-1+1&=&-3+1\\
x&=&-2
\end{array}$$

now you should sub x=-2 into the original equation to check that it works.

Interesting!

$$^7C_0(-1)^0(i)^7+
^7C_1(-1)^1(i)^6+
^7C_2(-1)^2(i)^5+
^7C_3(-1)^3(i)^4+
^7C_4(-1)^4(i)^3+
^7C_5(-1)^5(i)^2+
^7C_6(-1)^6(i)^1+
^7C_7(-1)^7(i)^0\\\\$$

$$=(i)^7+
7(-1)^1(i^2)^3+
^7C_2*1*(i^4)i+
^7C_3*-1*(i^2)^2+
^7C_4*1*(i^2)i+
^7C_5*-1*(i^2)+
7*1(i)^1+-1\\\\$$

$$=(-1)i+
7*-1*(-1)^3+
^7C_2*1*(-1)i+
^7C_3*-1*(-1)^2+
^7C_4*1*(-1)i+
^7C_5*-1*(-1)+
7*1*(i)^1+
-1\\\\$$

$$=-i+7+^7C_2(i)+
^7C_3(-1)+
^7C_4(-i)+
^7C_5(-1)+
7i
-1\\\\$$

$$=-i+7+21i
-35
-i35
+21
+7i
-1\\\\
=i(-1+21-34+7-1)+(7-35+21-1)\\\\
=i(-8)-8\\\\
=-8-8i$$

NOTE: I would actually be surprised if this is not riddled with careless errors. (I have fixed one little error)

BUT that is the technique that i would use.

Thanks admin.  

It is the distance from zero on the number line.

examples:

|6|=6

|-8|=8

-3*|-6+5|=-3*|-1|=-3*1=-3

I believe i already answered this, this morning (Australia time) just look through the other questions and answers.