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

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!

Answer 1

[David Hill]

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

Answer 2

[Álvaro]

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

[Walter Roberson]

Bob bought 0 apples??

[Álvaro]

'-'

Answer 3

[Image Analyst]

@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

[Álvaro]

Now I understand, thank you very much