Question

At an ice cream store, a family ordered 6 banana splits and 5 hot fudge sundaes, paying a total of $50 for their order. The next customer ordered 6 banana splits and 3 hot fudge sundaes and paid $42. How much does each item cost?​

Answer 1

The cost of a banana split is $5, and the cost of a hot fudge sundae is $4. This is determined by solving a system of equations representing the orders and total costs provided.

Step-by-step explanation:

The question involves solving a system of linear equations to find the price of each item at an ice cream store. Given that a family ordered 6 banana splits and 5 hot fudge sundaes, paying a total of $50, and the next customer ordered 6 banana splits and 3 hot fudge sundaes, paying $42, we can set up two equations to solve for the price of a banana split and a hot fudge sundae.

Let ‘b’ represent the cost of a banana split and ‘h’ represent the cost of a hot fudge sundae. We can write the following equations based on the information provided:

1. 
   
3. 6b + 5h = 50 (Equation 1 for the family’s order)
4. 
   
6. 6b + 3h = 42 (Equation 2 for the next customer’s order)

To solve these equations, we can use the method of subtraction to eliminate one variable. Subtract Equation 2 from Equation 1:

6b + 5h - (6b + 3h) = 50 - 42

6b + 5h - 6b - 3h = 8

2h = 8

h = 4

Now that we know the price of a hot fudge sundae (h) is $4, we can substitute this value into either Equation 1 or 2 to find the price of a banana split. Using Equation 2:

6b + 3(4) = 42

6b + 12 = 42

6b = 42 - 12

6b = 30

b = 5

So the cost of a banana split (b) is $5.