The local ice cream parlor sells small, medium, and large dishes of ice cream. One family

Question

purchased a small, medium, and large dish for $21. A second family purchased three small, one
medium, and one large dish for $31. A third family purchased one small, one medium, and two
large dishes for $31. Determine the price of each product size.

Answer 1

Let's assume the price of a small dish of ice cream is $x, the price of a medium dish is $y, and the price of a large dish is $z.

First, we can set up the following equations based on the information given:
1. For the first family: x + y + z = 21
2. For the second family: 3x + y + z = 31
3. For the third family: x + y + 2z = 31

To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method.

Subtracting equation 1 from equation 2, we get:
(3x + y + z) - (x + y + z) = 31 - 21
2x = 10
x = 5

Now, substitute the value of x back into equation 1 or 2:
x + y + z = 21
5 + y + z = 21
y + z = 16

Next, substitute the values of x and y into equation 3:
x + y + 2z = 31
5 + 16 + 2z = 31
21 + 2z = 31
2z = 10
z = 5

Therefore, the price of a small dish is $5, the price of a medium dish is $16, and the price of a large dish is $5.