Answer: 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.
