How do I put a word problem into a matrix?

Question

"Tasty Bakery sells three kinds of muffins: chocolate chip muffins at 20 cents each, oatmeal muffins at 25 cents each, and cranberry muffins at 30 cents each. Charles buys some of each kind and chooses three times as many cranberry muffins as chocolate chip muffins. If he spends $4.80 on 18 muffins, how many oatmeal muffins did he buy?"

I have been trying to solve this problem for a while, but it isn't making much sense to me. I'm supposed to put it into a matrix and solve it from there, but I don't even know how to get make a matrix out of that word problem. Please help as soon as possible, thanks!

Answer 1

x = number of cc muffins

y = number of oatmeal

z = number of cranberry



z = 3x

x + y + z = 18

20x + 25y + 30z = 480



rearrange the first so it lines up with the others, then drop off the variables and keep the coefficients

3x (+ 0y) - 1z = 0

1x + 1y + 1z = 18

20x + 25y + 30z = 480



3 0 -1 0

1 1 1 18

20 25 30 480



That's the matrix.

Answer 2

Matrix Story Problems

Answer 3

ignoring matrices for a moment, just writing the equations,

let number of choc chip = x

number of oatmeal = y

number of cranberry = z

count: x + y + z = 18

relation: -3x + z = 0

cost: 0.20x + 0.25y + 0.30z = 4.80

so as a matrix equation, AX = B, with A the coefficient matrix --



[ 1.....1......1 ] [ x ] .. [ 18 ]

[ -3 ... 0 ... 1 ] [ y] = [ ..0. ]

[.2... .25 .. .3 ] [ z ] ..[ 4.8]



so x = 3, y = 6, z = 9

that's 6 oatmeal muffins