Sarah would like to make a 6 lb nut mixture that is 60% peanuts and 40% almonds. she has several pounds of a mixture that is 80% peanuts and 20% almonds and several pounds of a mixture that is 50% peanuts and 50% almonds. a. what is the system that models this situation? b. what is the solution to the system? how many pounds of the 80/20 mixture? how many pounds of the 50/50 mixture?

a. The system that models this situation is,

x + y = 6 , 8 x + 5 y = 36.

b. Solution is x = 2lb and y = 4lb

where x is the quantity of 80% of peanuts mixture mix with y quantity of 50% of peanuts mixture for making 60% of peanuts mixture.

Step-by-step explanation:

Let x quantity of 80% of peanuts mixture mix with y quantity of 50% of peanuts mixture for making 60% of peanuts mixture.

Then According to the question,

x + y = 6       (1)

And, 80 % of x + 50 % of y = 60 % of 6

⇒ 0.8 x + 0.5 y = 3.6

⇒ 8 x + 5 y = 36   (2)

Where equation 1) and equation 2) are the required equation which models the given situation.

Now, 8 × equation 1)

We get, 8 x + 8 y = 48 (3)

equation (3) - equation (2)

we get, 3 y = 12

⇒ y = 4

By putting the value of y in equation (2)

we get, x = 2

Thus, he mixed 2 lb of mixture 80/20  and 4 lb of mixture 50/50 for making 6 lb of 50/50 mixture.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: