Trail Mix Packaging problem part 1.2
Ok, so here is my original problem from a book I am trying to learn. I can figure out the first part of the answer from @YukiJ however, I am unable to determine how the second part of the calculation was achieved:
First Part: You can solve the problem with any algorithm for a system of linear equations. If you want to calculate the solution by hand then things will get somewhat easier if you multiply each equation with 15 to remove the denominators:
$$7b+6s+2f=5700(raisins)$$
$$6b+4s+5f=7500(peanuts)$$
$$2b+5s+8f=9300(chocolate)$$
Second part: By adding the -$frac{6}{7}$ -multiple of the first equation to the second and the −$frac{2}{7}$ -multiple of the first equation to the third equation you obtain the following system:
$$Eq.one. 7b+6s+2f=5700 (raisins)$$
$$Eq.two. −frac{8}{7}s+frac{23}{7}f=frac{18300}{7} (peanuts)$$
$$Eq.three. frac{23}{7}s+frac{52}{7}f=frac{53700}{7} (chocolate)$$
I can not work out how the answer came out to 23 and 52 yet, this is my interpretation.
$$Att.one.Eq.two. frac{6 * -6}{7}b + frac{4 * -6}{7}s + frac{5 * -6}{7}f = frac{18300}{7} *$$
Could someone please break down the second part of the equation so I can understand it? $ *$ Definitely unsure how this value was attained.
Secondly, should I keep reading this book or is there another book that can help me with basic linear algebra that, would be more appropriate? Please base this second question after looking at the book attached to the "original problem" link above. Thanks again for your time.
linear-algebra
asked Dec 23 at 8:38
Conrad Thiele
205
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Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Ok, so here is my original problem from a book I am trying to learn. I can figure out the first part of the answer from @YukiJ however, I am unable to determine how the second part of the calculation was achieved:
First Part: You can solve the problem with any algorithm for a system of linear equations. If you want to calculate the solution by hand then things will get somewhat easier if you multiply each equation with 15 to remove the denominators:
$$7b+6s+2f=5700(raisins)$$
$$6b+4s+5f=7500(peanuts)$$
$$2b+5s+8f=9300(chocolate)$$
Second part: By adding the -$frac{6}{7}$ -multiple of the first equation to the second and the −$frac{2}{7}$ -multiple of the first equation to the third equation you obtain the following system:
$$Eq.one. 7b+6s+2f=5700 (raisins)$$
$$Eq.two. −frac{8}{7}s+frac{23}{7}f=frac{18300}{7} (peanuts)$$
$$Eq.three. frac{23}{7}s+frac{52}{7}f=frac{53700}{7} (chocolate)$$
I can not work out how the answer came out to 23 and 52 yet, this is my interpretation.
$$Att.one.Eq.two. frac{6 * -6}{7}b + frac{4 * -6}{7}s + frac{5 * -6}{7}f = frac{18300}{7} *$$
Could someone please break down the second part of the equation so I can understand it? $ *$ Definitely unsure how this value was attained.
Secondly, should I keep reading this book or is there another book that can help me with basic linear algebra that, would be more appropriate? Please base this second question after looking at the book attached to the "original problem" link above. Thanks again for your time.
linear-algebra
asked Dec 23 at 8:38
Conrad Thiele
205
New contributor
Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
New 2nd line: for column b : $6 - 6*7/7 = 0$. For column s: $4 - 36/7 = -8/7$ For column f $5 -12/7 = 23/7$ etc.
– Damien
Dec 23 at 10:24
OK, I think I am starting to get it. Here is equation with the co-ordinates: $$Eq2. frac{6_{21} - 6_{12}}{7_{11}} + frac{4_{22} * 7_{11} - 6_{12} * 6_{21}}{7_{11}} + frac{5_{23} * 7_{11} - 6_{12} * 2_{13}}{7_{11}}$$
– Conrad Thiele
Dec 24 at 3:01
The answer to the third equation does appear to be correct. $$frac{23}{7}s+frac{52}{7}f=frac{53000}{7} (chocolate)$$ I get 53000 compared with 53700. Btw @damien you explanation seems to give the right answer if you would like to mark it as the answer.
– Conrad Thiele
yesterday
Thank you for proposing. I have no time now to edit a clean answer. Good if I could help you
– Damien
yesterday
It is ok, I will ask another question showing my workings. Thank you for helping.
– Conrad Thiele
yesterday
add a comment |
Ok, so here is my original problem from a book I am trying to learn. I can figure out the first part of the answer from @YukiJ however, I am unable to determine how the second part of the calculation was achieved:
First Part: You can solve the problem with any algorithm for a system of linear equations. If you want to calculate the solution by hand then things will get somewhat easier if you multiply each equation with 15 to remove the denominators:
$$7b+6s+2f=5700(raisins)$$
$$6b+4s+5f=7500(peanuts)$$
$$2b+5s+8f=9300(chocolate)$$
Second part: By adding the -$frac{6}{7}$ -multiple of the first equation to the second and the −$frac{2}{7}$ -multiple of the first equation to the third equation you obtain the following system:
$$Eq.one. 7b+6s+2f=5700 (raisins)$$
$$Eq.two. −frac{8}{7}s+frac{23}{7}f=frac{18300}{7} (peanuts)$$
$$Eq.three. frac{23}{7}s+frac{52}{7}f=frac{53700}{7} (chocolate)$$
I can not work out how the answer came out to 23 and 52 yet, this is my interpretation.
$$Att.one.Eq.two. frac{6 * -6}{7}b + frac{4 * -6}{7}s + frac{5 * -6}{7}f = frac{18300}{7} *$$
Could someone please break down the second part of the equation so I can understand it? $ *$ Definitely unsure how this value was attained.
Secondly, should I keep reading this book or is there another book that can help me with basic linear algebra that, would be more appropriate? Please base this second question after looking at the book attached to the "original problem" link above. Thanks again for your time.
linear-algebra
asked Dec 23 at 8:38
Conrad Thiele
205
New contributor
Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ok, so here is my original problem from a book I am trying to learn. I can figure out the first part of the answer from @YukiJ however, I am unable to determine how the second part of the calculation was achieved:
First Part: You can solve the problem with any algorithm for a system of linear equations. If you want to calculate the solution by hand then things will get somewhat easier if you multiply each equation with 15 to remove the denominators:
$$7b+6s+2f=5700(raisins)$$
$$6b+4s+5f=7500(peanuts)$$
$$2b+5s+8f=9300(chocolate)$$
Second part: By adding the -$frac{6}{7}$ -multiple of the first equation to the second and the −$frac{2}{7}$ -multiple of the first equation to the third equation you obtain the following system:
$$Eq.one. 7b+6s+2f=5700 (raisins)$$
$$Eq.two. −frac{8}{7}s+frac{23}{7}f=frac{18300}{7} (peanuts)$$
$$Eq.three. frac{23}{7}s+frac{52}{7}f=frac{53700}{7} (chocolate)$$
I can not work out how the answer came out to 23 and 52 yet, this is my interpretation.
$$Att.one.Eq.two. frac{6 * -6}{7}b + frac{4 * -6}{7}s + frac{5 * -6}{7}f = frac{18300}{7} *$$
Could someone please break down the second part of the equation so I can understand it? $ *$ Definitely unsure how this value was attained.
Secondly, should I keep reading this book or is there another book that can help me with basic linear algebra that, would be more appropriate? Please base this second question after looking at the book attached to the "original problem" link above. Thanks again for your time.
linear-algebra
linear-algebra
asked Dec 23 at 8:38
Conrad Thiele
205
New contributor
Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 23 at 8:38
Conrad Thiele
205
New contributor
Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
asked Dec 23 at 8:38
Conrad Thiele
205
New contributor
Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 23 at 8:38
Conrad Thiele
205
asked Dec 23 at 8:38
Conrad Thiele
205
205
New contributor
Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Conrad Thiele is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
New 2nd line: for column b : $6 - 6*7/7 = 0$. For column s: $4 - 36/7 = -8/7$ For column f $5 -12/7 = 23/7$ etc.
– Damien
Dec 23 at 10:24
OK, I think I am starting to get it. Here is equation with the co-ordinates: $$Eq2. frac{6_{21} - 6_{12}}{7_{11}} + frac{4_{22} * 7_{11} - 6_{12} * 6_{21}}{7_{11}} + frac{5_{23} * 7_{11} - 6_{12} * 2_{13}}{7_{11}}$$
– Conrad Thiele
Dec 24 at 3:01
The answer to the third equation does appear to be correct. $$frac{23}{7}s+frac{52}{7}f=frac{53000}{7} (chocolate)$$ I get 53000 compared with 53700. Btw @damien you explanation seems to give the right answer if you would like to mark it as the answer.
– Conrad Thiele
yesterday
Thank you for proposing. I have no time now to edit a clean answer. Good if I could help you
– Damien
yesterday
It is ok, I will ask another question showing my workings. Thank you for helping.
– Conrad Thiele
yesterday
add a comment |
2
New 2nd line: for column b : $6 - 6*7/7 = 0$. For column s: $4 - 36/7 = -8/7$ For column f $5 -12/7 = 23/7$ etc.
– Damien
Dec 23 at 10:24
OK, I think I am starting to get it. Here is equation with the co-ordinates: $$Eq2. frac{6_{21} - 6_{12}}{7_{11}} + frac{4_{22} * 7_{11} - 6_{12} * 6_{21}}{7_{11}} + frac{5_{23} * 7_{11} - 6_{12} * 2_{13}}{7_{11}}$$
– Conrad Thiele
Dec 24 at 3:01
The answer to the third equation does appear to be correct. $$frac{23}{7}s+frac{52}{7}f=frac{53000}{7} (chocolate)$$ I get 53000 compared with 53700. Btw @damien you explanation seems to give the right answer if you would like to mark it as the answer.
– Conrad Thiele
yesterday
Thank you for proposing. I have no time now to edit a clean answer. Good if I could help you
– Damien
yesterday
It is ok, I will ask another question showing my workings. Thank you for helping.
– Conrad Thiele
yesterday
2
2
New 2nd line: for column b : $6 - 6*7/7 = 0$. For column s: $4 - 36/7 = -8/7$ For column f $5 -12/7 = 23/7$ etc.
– Damien
Dec 23 at 10:24
New 2nd line: for column b : $6 - 6*7/7 = 0$. For column s: $4 - 36/7 = -8/7$ For column f $5 -12/7 = 23/7$ etc.
– Damien
Dec 23 at 10:24
OK, I think I am starting to get it. Here is equation with the co-ordinates: $$Eq2. frac{6_{21} - 6_{12}}{7_{11}} + frac{4_{22} * 7_{11} - 6_{12} * 6_{21}}{7_{11}} + frac{5_{23} * 7_{11} - 6_{12} * 2_{13}}{7_{11}}$$
– Conrad Thiele
Dec 24 at 3:01
OK, I think I am starting to get it. Here is equation with the co-ordinates: $$Eq2. frac{6_{21} - 6_{12}}{7_{11}} + frac{4_{22} * 7_{11} - 6_{12} * 6_{21}}{7_{11}} + frac{5_{23} * 7_{11} - 6_{12} * 2_{13}}{7_{11}}$$
– Conrad Thiele
Dec 24 at 3:01
The answer to the third equation does appear to be correct. $$frac{23}{7}s+frac{52}{7}f=frac{53000}{7} (chocolate)$$ I get 53000 compared with 53700. Btw @damien you explanation seems to give the right answer if you would like to mark it as the answer.
– Conrad Thiele
yesterday
The answer to the third equation does appear to be correct. $$frac{23}{7}s+frac{52}{7}f=frac{53000}{7} (chocolate)$$ I get 53000 compared with 53700. Btw @damien you explanation seems to give the right answer if you would like to mark it as the answer.
– Conrad Thiele
yesterday
Thank you for proposing. I have no time now to edit a clean answer. Good if I could help you
– Damien
yesterday
Thank you for proposing. I have no time now to edit a clean answer. Good if I could help you
– Damien
yesterday
It is ok, I will ask another question showing my workings. Thank you for helping.
– Conrad Thiele
yesterday
It is ok, I will ask another question showing my workings. Thank you for helping.
– Conrad Thiele
yesterday
add a comment |
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2
New 2nd line: for column b : $6 - 6*7/7 = 0$. For column s: $4 - 36/7 = -8/7$ For column f $5 -12/7 = 23/7$ etc.
– Damien
Dec 23 at 10:24
OK, I think I am starting to get it. Here is equation with the co-ordinates: $$Eq2. frac{6_{21} - 6_{12}}{7_{11}} + frac{4_{22} * 7_{11} - 6_{12} * 6_{21}}{7_{11}} + frac{5_{23} * 7_{11} - 6_{12} * 2_{13}}{7_{11}}$$
– Conrad Thiele
Dec 24 at 3:01
The answer to the third equation does appear to be correct. $$frac{23}{7}s+frac{52}{7}f=frac{53000}{7} (chocolate)$$ I get 53000 compared with 53700. Btw @damien you explanation seems to give the right answer if you would like to mark it as the answer.
– Conrad Thiele
yesterday
Thank you for proposing. I have no time now to edit a clean answer. Good if I could help you
– Damien
yesterday
It is ok, I will ask another question showing my workings. Thank you for helping.
– Conrad Thiele
yesterday