Question

Arnold bought $19 worth of flavored milk. He bought a total of 24 cartons. Strawberry milk costs $1 and chocolate milk costs $0.50. How many of each flavor did he buy?

Mike says Arnold bought 14 strawberry milks and 10 chocolate milks.
Kate says Arnold bought 16 strawberry milks and 3 chocolate milks.

Answer 1

To determine how many cartons of each flavor Arnold bought, we set up a system of equations based on the information provided:

Let:
- \( s \) = the number of strawberry milk cartons
- \( c \) = the number of chocolate milk cartons

We have the following equations based on the problem:

1. The total number of cartons:
\[
s + c = 24
\]

2. The total cost of the milk:
\[
1s + 0.5c = 19
\]

We can simplify the second equation by multiplying everything by 2 to eliminate the decimal:
\[
2s + c = 38
\]

Now we have a system of equations:
1. \( s + c = 24 \)
2. \( 2s + c = 38 \)

Next, we can solve this system. We can subtract the first equation from the second equation:

\[
(2s + c) - (s + c) = 38 - 24
\]
This simplifies to:
\[
s = 14
\]

Now, substituting \( s = 14 \) back into the first equation to find \( c \):
\[
14 + c = 24
\]
\[
c = 10
\]

Thus, Arnold bought 14 cartons of strawberry milk and 10 cartons of chocolate milk.

Now, let's verify what Mike and Kate said:

- **Mike's claim:** 14 strawberry milks and 10 chocolate milks - **This is correct.**
- **Kate's claim:** 16 strawberry milks and 3 chocolate milks - **This is incorrect.**

So the solution is:
Arnold bought **14 cartons of strawberry milk and 10 cartons of chocolate milk.**