math, finite mathematics

My question is that i need help for this problem understanding how they came about to the answer it is an odd problem so:

18 cakes for the first one.
8 cakes for the second one.
2 cake for the third one.

Here is the original problem:
A baker sells three types of cakes, each requiring the amount of ingredients shown.

Ingredients / cake 1 / cake 2/cake 3
Flour (cups)/ 2 / 4 / 2
Sugar (cups)/ 2 / 1 / 2
Eggs / 2 / 1 / 3

To fill its orders for these cakes,the baker used 72cups of flour, 48 cups of sugar, and 50 eggs. How many cakes of each type were made?

Three unknowns, three equations
Flour equation:2C1 + 4C2 + 2 C3=72
Sugar equation:2C1 +1C2 + 2C3=48
Egg equation:2C1 +C2 + 3C3=50

solve for C1, C2, C3
You have a problem here on equation 1 and equation 2. They are not independent equations in variables C1,C3.So you can only use them once.
subtract2 from 1 to get C2=8
Now you have to shift to equations 3 and one of the first two.
2C1 +8 + 3C3=50 or 2C1 + 3C3=42
I'll pick equation1 for the other.
2C1 + 32 + 2 C3=72 or 2C1 + 2 C3=40
subtract those equations to get C2=2
finally, you have to stay away from equaton1, 2 because you have already used it, so in equation 3
2C1 +8 + 6=50 or C1=18
This is not a good problem to use in a text because of the linear dependence problem in equations 1,3

x_i = number of cakes of type i

72 cups of flour were used --->

2 x1 + 4 x2 + 2 x3 = 72 (1)

48 cups of sugar were used --->

2 x1 + x2 + 2 x3 = 48 (2)

50 eggs were used --->

2 x1 + x2 + 3 x3 = 50 (3)

(1) - (2):

3 x2 = 24 -->

x2 = 8

(3) - (2):

x3 = 2

Insert these values of x3 and x2 in any of the three equations to obtain:

x1 = 18

thank you i figured it out and understand it thanks to your explanation. You sure have helped me.

1. 👍 0
2. 👎 0
3. 👁 225
1. ye that is pretty hard

1. 👍 0
2. 👎 0
posted by bObella

Similar Questions

1. math

I'm having problem understanding 2 2/7-1 1/3= can somebody help me with this question.

asked by cora evans on December 24, 2013
2. Math

Hey! So, I've been working on this problem for awhile but I'm currently a bit dumbfounded on how to solve it. I think this question has been answered before but I still don't quite understand how it works or how to explain it. The

asked by Z on June 20, 2016
3. Psychology

I am having trouble understanding the following question: What prevents an individual from allocating attention the way in which they intend? Can someone give me a better understanding of the question?

asked by Lynn on January 19, 2010
4. Algebra

Not understanding the question. Why a solution of a word problem should be checked using the original wording of the problem and not the equation written from the wording.

asked by Cindy on February 2, 2011
5. math

I'm having problem understanding this question. 29.64 acres= hectares, can somebody tell me if 11.9949 is the right answer yes or no.

asked by cora evans on January 13, 2014
6. MATH

I'm sure what if this is the right answer that the question is looking for. since my eng. not that good i have hard time understanding. Please help me. Question: write a situation that can be modeled by the following linear

asked by may on March 31, 2015
7. Algebra

I am not understanding your question. This is what the problem is (-7y^2-4y+6)=(7y^2-4y-4)-(2y^2-2y-6)Simplifying a sum or difference of three univariate polynomials

asked by Kindra Spirit on December 2, 2015
8. algebra

I am not understanding your question. This is what the problem is (-7y^2-4y+6)=(7y^2-4y-4)-(2y^2-2y-6)Simplifying a sum or difference of three univariate polynomials

asked by Kindra Spirit on December 2, 2015
9. English Analysis

Reading The Stranger by the lovely Albert Camus. Just need help understanding this question: -After I listed some themes I explored, my teacher asks: "Given the themes you listed, are any conventions questioned based on the

asked by Albert on October 9, 2012
10. math

I'm not understanding this problem. Write the rate in lowest terms. A printer can print 3 pages in 12 seconds. I need somebody to help me with this question.

asked by cora evans on January 4, 2014
11. probability

You guess on all of the answers on a 10 question quiz. If there are 4 possible answers for each question, what is the probability that you get 3 questions right? i've tried doing this problem multiple times and i'm just not

asked by shyanne on May 10, 2016

More Similar Questions