Question

please help?


A milkshake vendor sold 16 mango shakes, 13 strawberry shakes, and 29 chocolate shakes during the first shift of the day. In the second shift, she sold 26 mango shakes, 19 strawberry, and 45 chocolate. In the last shift, she sold 6 mango shakes, 11 strawberry, and no chocolate. Total sales were $419 in the first shift, $649 in the second shift, and $96 in the third shift. If you form a linear system representing this data and create a matrix from it, the determinant is 578. What is the price of one chocolate shake

Answer 1

BBW!!!

Answer 2

bbw?

Answer 3

yes

Answer 4

whats that?

Answer 5

big beautiful women :DD

Answer 6

?

Answer 7

nvm -.-

Answer 8

get out of here @sourwing this ain't a place to hit on a women

Answer 9

Do you know how to set up a linear system representing this information?

Answer 10

im supposed to use a
Matrices

Answer 11

Right. Do you know how to set up a matrix which describes the sales of the 3 shifts?

Answer 12

16 13 29
26 19 45
06 11 0

Answer 13

Yes. And if we multiply that by

m
s
c

we'll get

419
649
96

Answer 14

so
16m+13s+29c=419
26m+19s+45c=649
6m+11s=96

Answer 15

Yes, those would the equations.

It's a little unclear to me if you're expected to solve them in any particular fashion, but probably using one of the methods to solve a matrix would be the best.

Answer 16

im supposed to solve for c
but I don't know what determinant 578 is

Answer 17

Yes, I know you are supposed to solve for \(c\). But there are a number of ways you could do so, and the problem author might have a particular one in mind...

The determinant of the matrix you constructed is 578. The determinant of a 3x3 matrix such as you have:

\[\left(
\begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i \\
\end{array}
\right)\]is given by \[\text{det} = ( aei + bfg + cdh) - (ceg + bdi + afh\]
You can see that this is just starting at the upper left corner, multiplying diagonally down to the right, then moving one spot along the top to the next column and doing the same (except "wrapping around" to the left side as needed), and finally doing the same from the top of the 3rd column. Then you do the same thing going in the other direction, and subtract these three from the previous three.

\[16*19*0 + 13*45*6 + 29*26*11\]\[\qquad - 29*19*6 - 13*26*0 - 16*45*11 = 578\]

Answer 18

Now, there's something called Cramer's rule which we can use with our matrix and the determinant to find the values of \(m,s,c\) with relatively little pain. Have you heard of it?

Answer 19

http://www.purplemath.com/modules/cramers.htm

Answer 20

Cramer's rule says that if we've set up the matrix as we have here, you can find the values of \(m,s,c\) by replacing each column of the matrix in turn by the column representing the sales totals, finding the determinant of that matrix, and dividing by the determinant of the matrix before we changed anything.

To find the price of a mango shake, for example,

419 13 29
649 19 45
96 11 0

Determinant of that is

419*19*0 + 13*45*96 + 29*649*11 - 29*19*96 - 13*649*0 -419*45*11 = 2890

2890/578 = 5, so a mango shake costs $5

Answer 21

Do the same, except place the sales column in the 3rd column, and you'll find out that they are selling an outrageously expensive chocolate shake!

Answer 22

its 9

Answer 23

yes, that's what I get both with Cramer's rule and solving it another way.

Answer 24

ok thank you so much!!!!!!!