Question

An animal breeder can buy four types of food for Vietnamese pot-bellied pigs. Each case of Brand A contains 35 units of fiber, 40 units of protein, and 40 units of fat. Each case of Brand B contains 140 units of fiber, 120 units of protein, and 120 units of fat. Each case of Brand C contains 245 units of fiber, 200 units of protein, and 220 units of fat. Each case of Brand D contains 420 units of fiber, 360 units of protein, and 340 units of fat.

Answer 1

How many cases of each brand should the breeder mix together to obtain a food that provides 4305 units of fiber, 3600 units of protein, and 3780 units of fat? Let x represent the number of cases of brand A, y represent cases of brand B, z represent the cases of brand C, and w represent the number of cases of brand D. There are 4 ways in which the breeder can mix brands to obtain a food that provides 4305 units of fiber, 3600 units of protein, and 3780 units of fat.

Answer 2

sounds like simultaneous equations with 3 variables, fiber, protein and fat.

Answer 3

@triciaal yea, i set up equations
35x+140y+245z+420w= 4305
40x+120y+200z+360w =3600
40x+120y+220z+340w=3780
for the different variables and i'm supposed to use matrices i got confused in the third step, i got to this point:

35 140 245 420 4305
40 120 200 360 3600
40 120 220 340 3780

1 4 7 12 123
40 120 200 360 3600
40 120 220 340 3780

but im not quite sure how to do the next part

Answer 4

I'm not good with solving using matrices finding the zero matrix but if you want to verufy the solution you can solve otherwise use 2 equations and eliminate one variable use another 2 and eliminate the same variable now solve 2 variable simultaneous use the value in the expression for the variable eliminated
regardless of which method you use to solve, always good practice to check values in any of the originals

Answer 5

@Mehek14 can you take this?

Answer 6

@imqwerty

Answer 7

In my experience, matrices was easier than solving these by elimination. Much less groundwork

Answer 8

yea i got that at one point in the process, and then i got:
1 4 7 12 123
40 120 200 360 3600
40 120 220 340 3780


1 4 7 12 123
0 -40 -160 -280 -480

but then i got lost

Answer 9

well there are 4 variables and only 3 equations
that seems like a problem

Answer 10

oh ok, i thought because there was 3 different types of food and 4 brands there would only be three equations

Answer 11

did i set the equations up wrong if there's supposed to be 4?

Answer 12

nope they seem okay but still check once again and you need to use matrix row-echelon thing here

Answer 13

this video explains how you solve system of 3 linear equations to find 4 unknowns-

https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/matrices-elimination/v/matrices-reduced-row-echelon-form-1

Answer 14

ok im watching it now, thanks!