Hello! I need some help solving linear equations for the coefficients

Question

Xenon Asuncion 2020-9-5

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评论： Álvaro 2023-12-1

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This is the question:

Liz buys three apples, a dozen bananas, and one cantaloupe for $2.36.

Bob buys a dozen apples and two cantaloupe for $5.26.

Carol buys two bananas and three cantaloupe for $2.77.

How much do single pieces of each fruit cost?

This is my work so far:

%Set the variables to be used in the problem.
syms x y z
%Input the equations given in the problem.
Equation_1 = input('Input the given equation. To input the total amount use "==". ')
Equation_2 = input('Input the given equation. To input the total amount use "==". ')
Equation_3 = input('Input the given equation. To input the total amount use "==". ')
%Transform the linear equation into a matrix form
[A, B] = equationToMatrix ([Equation_1, Equation_2, Equation_3], [x, y, z])

I tried running it, but it errors when I put the equation. Thanks in advance!

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Answer 1

David Hill 2020-9-5

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a=[3 12 1;12 0 2;0 2 3]\[2.36;5.26;2.77];

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Answer 2

Álvaro 2023-11-30

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编辑：Image Analyst 2023-11-30

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Hi, I tried the following code (I do not know why, but one of the prices is less than zero)

x = [ 3 12 1; 0 12 2; 0 2 3];
y = [2.36; 5.26; 2.77];
v = linsolve(x,y)
v = 3×1
   -0.7300
    0.3200
    0.7100

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Walter Roberson 2023-11-30

Bob bought 0 apples??

Álvaro 2023-12-1

'-'

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Answer 3

Image Analyst 2023-11-30

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@Álvaro you should have done it like this:

% Liz buys three apples, a dozen bananas, and one cantaloupe for $2.36. 
% Bob buys a dozen apples and two cantaloupe for $5.26. 
% Carol buys two bananas and three cantaloupe for $2.77. 
% How much do single pieces of each fruit cost?
% 2.36 = 3 * a + 12 * b + c
% 5.26 = 12 * a + 0 * b + 2 * c
% 2.77 = 0 * a + 2 * b + 3 * c
% totals = quantities * individualPrices
% Create arrays that describe the set of linear equations:
totals = [2.36; 5.26; 2.77]
totals = 3×1
    2.3600
    5.2600
    2.7700
quantities = [3, 12, 1;
    12, 0, 2;
    0, 2, 3]
quantities = 3×3
     3    12     1
    12     0     2
     0     2     3
individualPrices = linsolve(quantities,totals)
individualPrices = 3×1
    0.2900
    0.0500
    0.8900
% Double check:
totalsCheck = quantities * individualPrices
totalsCheck = 3×1
    2.3600
    5.2600
    2.7700