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 bough 16 strawberry milks and 3 chocolate milks.

Use the guess and check method to determine if who has the correct solution.

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 bough 16 strawberry milks and 3 chocolate milks.

Mike

Arnold

Answer 1

Let \( x \) be the number of cartons of strawberry milk and \( y \) be the number of cartons of chocolate milk. We have the following equations based on the information given:

1. The total number of cartons: \[ x + y = 24 \]

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

Now, we'll check both Mike's and Kate's assertions using these equations.

Checking Mike's solution:

Mike claims Arnold bought 14 strawberry milks and 10 chocolate milks:

• \( x = 14 \)
• \( y = 10 \)

Substituting into the first equation: \[ 14 + 10 = 24 \] This satisfies the first equation.

Now check the second equation: \[ 1(14) + 0.5(10) = 14 + 5 = 19 \] This satisfies the second equation.

So, Mike's solution is correct.

Checking Kate's solution:

Kate claims Arnold bought 16 strawberry milks and 3 chocolate milks:

• \( x = 16 \)
• \( y = 3 \)

Substituting into the first equation: \[ 16 + 3 = 19 \] This does not satisfy the first equation since it needs to equal 24.

Thus, Kate's solution is incorrect.

Conclusion:

Mike is correct. Arnold bought 14 strawberry milks and 10 chocolate milks.