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.
Accepted Solution
A:
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 = xThe carbs in each snack bar = ySo, 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 = 89Similarly, 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 = 93Solving 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 + 279or, - 7 y = -77⇒ y = 77 / 7 = 11 , or y = 11Putting this in (1) , we get 3 x + 4y = 89 ⇒ 3 x + 4(11) = 89 or, 3 x = 89 - 44 = 45or, x = 45/3 = 15⇒ x = 15Hence, there are 15 carbs in each glass of milk.There are 11 carbs in each snack bar.