Calculation of 3 eqns at once and calculating the cost of the three items given the total

Hi all i am trying to calculate a question regarding the prices of each item if you are given a total.

how would i calculate the prices of items given that:

Ben spent $18.25 on one pizza, five cans of coke and two bars of chocolate.

Jez spent $17.30 while buying two pizzas, one can of coke and three bars of chocolate.

Cath spent $23.50 while buying three pizzas, seven cans of soft drink and one chocolate bar.

i need to calcualte individual price for the three items and formulate the equations

im not sure where to start with this and any help would be greatly appreciated!

thanks in advance.

[Chunru]

Assume the price of a pizza is x_1, the price of a can of coke is x_2 and a bar of choc is x_3. Can you writhe a system of equations? Then think of a matrix form of the equation of the form Ax=b. MATLAB is very good at solving such equation: x=A\b. Try it out with these hints.

[Walter Roberson]

1*pizza + 5*coke + 2 * chocolate == 18.25

implies

[1 5 2] * [pizza; coke; chocolate] == 18.25

[Joe Ainsworth]

%  define the coefficient matrix
Coefficients = [1, 2, 3; 1, 2, 3; 1, 2, 3];
%  define the vector of knowns
Knowns = [18.25; 17.30; 23.50];
% calculate unknowns
Unknowns = Coefficients \ Knowns;

@Chunru like this?

[Walter Roberson]

Coefficients should not be all the same [1 2 3] . For example first row should be [1 5 2]

[Joe Ainsworth]

@Walter Roberson so i can just randomise and there is not effect?

[Joe Ainsworth]

%  define the coefficient matrix
[1 5 2] * [pizza; coke; chocolate] == 18.25
[6 8 3] * [pizza; coke; chocolate] == 17.30
[5 4 9] * [pizza; coke; chocolate] == 23.50

@Walter Roberson @Chunru how does this look

[Joe Ainsworth]

not sure where to go from here now

[Joe Ainsworth]

A = [1 5 2;6 8 3; 5 4 9]
B = [18.25; 17.30; 23.50]
X = A\B

[Walter Roberson]

Cath spent $23.50 while buying three pizzas, seven cans of soft drink and one chocolate bar.

Where is "seven" of something encoded in your A matrix?

A = [1 5 2;6 8 3; 5 4 9]

A = 3×3

1 5 2 6 8 3 5 4 9

B = [18.25; 17.30; 23.50]

B = 3×1

18.2500 17.3000 23.5000

X = A\B

X = 3×1

-2.5832 3.0991 2.6689

B_reconstruct = A*X;
compose("%d pizza @ $%.2f each + %d soft drink @ $%.2f each + %d chocolate bar at $%.2f each = $%.2f", A(:,1), X(1), A(:,2), X(2), A(:,3), X(3), B_reconstruct(:))

ans = 3×1 string array
    "1 pizza @ $-2.58 each + 5 soft drink @ $3.10 each + 2 chocolate bar at $2.67 each = $18.25"
    "6 pizza @ $-2.58 each + 8 soft drink @ $3.10 each + 3 chocolate bar at $2.67 each = $17.30"
    "5 pizza @ $-2.58 each + 4 soft drink @ $3.10 each + 9 chocolate bar at $2.67 each = $23.50"

If your pizza is coming out at a negative price, you have probably done something wrong.

... DId Jez really buy 6 pizzas ??

[Joe Ainsworth]

worked it out @Walter Roberson thanks for the help