Question

Two glasses of milk and 3 snack bars have a total of 62 carbohydrates, and 3 glasses of milk and 2 snack bars have a total of 58 carbs. Determine how many carbs are in one glass of milk in one snack bar.

Answer 1

Step-by-step explanation:

So looking at this question, we have two variables (1 - a glass of milk; 2 - a snack bar) and two equations to use to solve for the two variables. Remember that for any number of variables, you need that same number or more equations to solve for the variables.

Let's say that a glass of milk is represented by g and a snack bar is represented by s.

So we essentially have two equations here:

4 glasses of milk + 3 snack bars = 88 carbs, or:

4g + 3s = 88

2 glasses of milk + 4 snack bars = 74 carbs, or:

2g + 4s = 74

Now that we have this, we can solve for our equations. There are two ways to do this:

SUBSTITUTION - solve for one variable, then substitute it in

Let's solve for g using the second equation. First, we'll isolate g by subtracting 4s from both sides.

2g = 74 - 4s

Next, we can divide the whole equation by 2 to solve for g.

g = 37 - 2s

Now, we can substitute this into the first equation for g and solve for s.

4g + 3s = 88

4(37 - 2s) + 3s = 88

148 - 8s + 3s = 88

148 - 5s = 88 (now subtract 88 from both sides and add 5s to both sides)

60 = 5s

s = 12

Now we can use this to solve for g in the original equation

g = 37 - 2s

g = 37 - 2(12) = 37 - 24 = 13

ELIMINATION - eliminate one variable to solve for the other, then use that to solve for the first

Let's look at our two equations

4g + 3s = 88

2g + 4s = 74

Let's eliminate the variable g first by multiplying the second question by -2.

4g + 3s = 88

-4g - 8s = -148

If we add these two equations together, we get

-5s = -60

Divide both sides by -5 and we get

s = 12

Now, we can plug s into either equation to solve for g as we did above.