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 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.