Question

Four glasses of milk and 2 snack bars have a total of 86 carbohydrates​ (carbs), and 2 glasses of milk and 3 snack bars have a total of 69 carbs. Determine how many carbs are in one glass of milk and in one snack bar.

Answer 1

One glass of milk: 15 carbs

One snack bar: 13 carbs

Explanation:

This problem is an example of systems of linear equations. We can set this problem up by defining variable. I used
`m` for the glass of milk and
`b` for the snack bar.

First, we have: 4 glasses of milk and 2 snacks bar have a total of 86 carbs. We can write this as

`4m+2b=86`

Next: 2 glasses of milk and 3 snack bars have a total of 69 carbs.

We can write this as

`2m+3b=69`

Now we set it up.

`4m+2b=86`

`2m+3b=69`

By dividing both sides of the first equation by 2, we can use the subtraction method to get rid of the variable
`m`. Now we have

`2m+b=43`

`2m+3b=69`

Subtract like terms and solve for
`b`

`-2b=-26`

`b=13`

Now we substitute
`b` back into the original equation to find
`m`.

`2m+(13)=43`

`2m=30`

`m=15`

There you have it. I hope this helps!