At an ice cream store, a family ordered 4 banana splits and 4 hot fudge sundaes, paying a total of $36 for their order. The next customer ordered 4 banana splits and 6 hot fudge sundaes and paid $44. How much does each item cost?

The price for each banana splits is $5 and that for each hot fudge sundaes is $4.

Step-by-step explanation:

Let the price for each banana splits is $x and that of each fudge sundaes is $y.

The total price of 4 banana splits and 4 hot fudge sundaes is $36 and the total price of 4 banana splits and 6 hot fudge sundaes is $44.

Therefore, we get the equations

4x + 4y = 36 ... (1) and

4x + 6y = 44 ... (2)

Solving equations (1) and (2) we get 2y = 8, ⇒ y = $4

Now, from equation (1), we get

x = 9 - y = 9 - 4 = $5

Therefore, the price for each banana splits is $5 and that for each hot fudge sundaes is $4. (Answer)