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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.At an ice cream store, a family ordered banana split, paying a total of for their order. The next customer ordered banana splits and hot fudge sundaes and paid . How much does each item cost?A banana split costs and a hot fudge sundae costs .
Full solution
Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.At an ice cream store, a family ordered banana split, paying a total of for their order. The next customer ordered banana splits and hot fudge sundaes and paid . How much does each item cost?A banana split costs and a hot fudge sundae costs .
- Define Variables: Let be the cost of a banana split and be the cost of a hot fudge sundae.First family's order: banana split () for .
- First Family's Order: Next customer's order: banana splits and hot fudge sundaes for .
- Next Customer's Order: Create an augmented matrix to represent the system of equations:\begin{array}{cc|c} 1 & 0 & 6 \ 4 & 6 & 54 \ \end{array}
- Create Augmented Matrix: Use row operations to find the cost of each item.First, multiply the first row by and add it to the second row to eliminate from the second equation.
- Use Row Operations: Now we have the new system of equations:
- New System of Equations: Solve for by dividing the second equation by .
- Solve for : Substitute into the first equation to solve for .
