Question

two glasses of milk and three snack bars have a total of 66 carbs and three glasses of milk and two snack bars have a total of 64 carbs determine how many carbs are in one glass of milk and one snack bar

Answer 1

A system of equations is used to find that one glass of milk contains 12 carbohydrates and one snack bar contains 14 carbohydrates.

Step-by-step explanation:

The student is asking a system of equations problem where we need to find the number of carbohydrates in one glass of milk and one snack bar. To solve this problem, we let 'm' represent the number of carbs in a glass of milk and 's' represent the number of carbs in a snack bar. The two equations based on the information given would be:

• 2m + 3s = 66
• 3m + 2s = 64

After solving the system of equations, we find that one glass of milk contains 20 carbs and one snack bar contains 12 carbs.

To solve the system, we can multiply the first equation by 3 and the second by 2 to eliminate one of the variables:

• (2m + 3s) * 3 → 6m + 9s = 198
• (3m + 2s) * 2 → 6m + 4s = 128

Subtracting the second resulting equation from the first:

• 6m + 9s - (6m + 4s) = 198 - 128
• 5s = 70
• s = 14

Now we substitute 's = 14' back into the initial first equation:

• 2m + 3(14) = 66
• 2m + 42 = 66
• 2m = 24
• m = 12

Seems like there was a mistake in calculating the values for 'm' and 's'. Let's revisit the calculations:

• 5s = 70 → s = 14 was correct.
• Let's substitute 's = 14' into the second initial equation:
• 3m + 2(14) = 64
• 3m + 28 = 64
• 3m = 36
• m = 12

Now we have the right values: a glass of milk contains 12 carbs and a snack bar contains 14 carbs.