Part 1 of 2 Question: Three glasses of milk and 4 snack bars both have 86 carbs, and 4 glasses of milk and 3 snack bars both have of 82 carbs. How many carbs are in 1 glass of milk and one snack bar

Answer 1

Let x be the number of carbs in one glass of milk, y be the number of carbs in one snack bar, we can have a system of equations:

3x+4y=86

4x+3y=82

2.Solve the system, we have x = 10 and y = 14.

3.x + y = 24 calories is the answer.

Answer 2

Hi Joaquin. My name is Ashley and I have broken down the problem below. Please let me know if you have any questions. The method here is to create equations, find the number of carbs in one glass of milk and 1 snack bar, and add them together at the end.

Step 1: Label your variables or your unknowns.

g- # of carbs in 1 glass of milk

b- # of carbs in 1 snack bar

Step 2: Create Equations. Since we have 2 variables, we need 2 equations. The equations are created based on the information the problem gave us

3 glasses + 4 bars = 86 carbs

3g+ 4b = 86

4 glasses + 3 bars = 82 carbs

4g+ 3b= 82

Step 3: Solve the Equations

Let's start with the elimination method and eliminate g.

3g+4b=86

4g+3b=82

We want to cancel g so we want to make sure that the number in front of g is equal with opposite signs.

-4(3g+4b=86)

3(4g+3b=82)

-12g-16b=-344

12g + 9b = 246

Add both equations. The g cancels out and you are left with b and the other side of the equation.

-12g - 16b = -344

12g + 9b = 246

Isolate b.

-7b = -98

-7b/(-7) = -98/(-7)

b = 14

Let's substitute b back into one of the original equations, so we can find g.

3g+4b=86

3g+4(14)=86

3g+56=86

3g= 86-56

3g=30

g=10

Step 4: Do a quick check by plugging both values into the original equation to make sure both sides are equal.

4g + 3b = 82

4(10) + 3(14)= 82

40+42 = 82

Step 5: Finally, remember that the problem wanted the number of carbs in one snack bar and one glass of milk. We have to add the values we found.

g + b = ?

10 + 14 = 24

There are 24 carbs in one glass of milk and one snack bar. I hope this helps.

Answer 3

Let x = the number of carbs in a glass of milk

y = the number of carbs in a snack bar

3x+4y=86 represents the first scenario

4x+3y=82 represents the second scenario

Solving by elimination means that when the equations are added together a variable must cancel, so lets multiply the top equation by -4 and the bottom equation by 3

-4(3x+4y=86) = -12x-16y=-344

3(4x+3y=82) = 12x+9y=245

Now let's add the new equations together

-12x-16y=-344

+ 12x+9y=245

-------------------------

-7y=-99

Dividing both sides by -7 gives us

y=14.14 calories

plugging into the original equation:

3x+4(14.14)=86

3x+56.57=86

Now lets subtract 56.57 from each side

3x=29.43

And divide by three on both sides

x=9.81 calories

Therefore:

A glass of milk has 9.81 calories and a snack bar has 14.14 calories.