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?

Question

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.