Question

Three glasses of milk and 4 snack bars have a total of 89 carbohydrates​ (carbs), and 4 glasses of milk and 3 snack bars have a total of 9393 carbs. Determine how many carbs are in one glass of milk and in one snack bar.

Answer 1

Answer:

There are  15 carbs in each glass of milk and  11 carbs in each snack bar.

Step-by-step explanation:

Let us assume:

The carbs in  each glass of milk  = x

The carbs in each snack bar = y

So, the carbs in 3 glass of milk = 3 ( Carbs in 1 glass of milk )  = 3 x

and the carbs in 4 snack bars  = 4 ( Carbs in 1 snack bar)  = 4 y

⇒ 3 x + 4 y = 89

Similarly, the carbs in 4 glass of milk = 4 ( Carbs in 1 glass of milk )  = 4 x

and the carbs in 3 snack bars  = 3 ( Carbs in 1 snack bar)  = 3 y

⇒ 4 x + 3 y = 93

Solving the given system of equation:

3 x + 4 y = 89     ............(1)

4 x + 3 y = 93    ............. (2)

Multiply equation (1) with (-4) , and (2) by 3 and add both equation.

-12 x - 16 y + 12 x + 9 y = -356 + 279

or, - 7 y = -77

⇒ y =  77 / 7 = 11 , or y  =   11

Putting this in (1) , we get  3 x  + 4y = 89

⇒ 3 x  + 4(11) = 89  or,  3 x =  89 - 44 = 45

or, x = 45/3  = 15

⇒ x = 15

Hence, there are  15 carbs in each glass of milk.

There are  11 carbs in each snack bar.