AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.At an ice cream store, a family ordered banana splits and hot fudge sundaes, 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 any method, and fill in the blanks.At an ice cream store, a family ordered banana splits and hot fudge sundaes, 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 Costs: Let's denote the cost of a banana split as dollars and the cost of a hot fudge sundae as dollars.
- First Equation: According to the problem, banana splits and hot fudge sundaes cost . This gives us the first equation:
- Second Equation: The next customer ordered banana splits and hot fudge sundaes for , which gives us the second equation:
- Solve System: We now have a system of equations:We can solve this system using the elimination method by subtracting the first equation from the second equation to eliminate .
- Subtract Equations: Subtracting the first equation from the second equation:
- Find y: Now that we have the value of , we can substitute it back into one of the original equations to find . Let's use the first equation:
