Two glasses of milk and 3 snack bars have a total of 61 carbohydrates (carbs), and 4 glasses of milk and 2 snack bars have a total of 70 carbs. Determine how many carbs are in one glass of milk and in one snack bar.

24 carbohydrates

Step-by-step explanation:

Represent Snack bars with S and Milks with M.

So, we have:

and

Required: Solve for M and S

Convert the given expressions to mathematical expressions:

--- (1)

--- (2)

Multiply the first equation by 2

--------- * 2

--- (3)

Subtract (1) from (3)

Solve for S

Substitute 13 for S in (2)

Solve for 4M

Solve for M

1 glass of milk and 1 snack bar = S + M

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240