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

[M.Adhithya]

The vectors a, b, and c represent the number of apples, bananas, and cherries (respectively) sold by Fruit Barn on various days. Given the following MATLAB command and its result, the sales of which two fruits are the most correlated?

corrcoef([a b c])

ans =

1.0000 0.4356 -0.0303

0.4356 1.0000 0.1079

-0.0303 0.1079 1.0000

[Image Analyst]

@M.Adhithya It's the fruits represented by the largest non-1 number, right?

This looks like a homework problem. If you have any questions ask your instructor or read the link below to get started:

How do I get help on homework questions on MATLAB Answers? - MATLAB Answers - MATLAB Central

Obviously, if it is homework, we can't give you the full solution because you're not allowed to turn in our code as your own.

In the meantime check out max and find.