SOLUTION: You and two friends bought annual flowers, perennial flowers and tree seedlings at a local nursery. You have lost your receipts and only have your credit card bills with the total

Question 62117This question is from textbook Applied College Algebra
: You and two friends bought annual flowers, perennial flowers and tree seedlings at a local nursery. You have lost your receipts and only have your credit card bills with the total of each order. You bought 10 annuals and 4 perennials. Your total cost was $21. Alex bought 24 annuals and 3 perennials for a total for a total of $24. Petra bought 16 annuals, 2 perennials, and 3 seedlings for $25. How much did each item cost?
a. Set up a system of equations to solve for the prices of the items above. Define your variables as a, p, and s for the prices of annuals,perennials, and tree seedlings, respectively.
b. Convert your system to a matrix equation and solve the system using inverse matrices.
c.Solve the system by using Cramer's Method.
d. Solve the system of linear equations using linear combinations. This question is from textbook Applied College Algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You bought 10 annuals and 4 perennials. Your total cost was $21. Alex bought 24 annuals and 3 perennials for a total for a total of $24. Petra bought 16 annuals, 2 perennials, and 3 seedlings for $25. How much did each item cost?
a. Set up a system of equations to solve for the prices of the items above. Define your variables as a, p, and s for the prices of annuals,perennials, and tree seedlings, respectively.
10a+4p+0s=21
24a+3p+0s=24
16a+2p+3s=25
AX=B
X=A^(-1)B
X=[0.71,3.47.2.22]
Price of annuals = 71 cents
Price of perennials = 3.47 dollars
Price of seedlings = 25 cents
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Cheers,
Stan H.
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