The value of y varies directly with x. When the value y is ⅗, the value of x is 0.125. What is the value of x when the value of y is 12?

x = 2.5

Step-by-step explanation:

y varies directly with x means the times that y increases, the times x increases and vice versa.

If y increases from 3/5 to 12 is being increased:

12 / 3/5 = 20 times

Thus, the value of x is being increased by definition, also 20 times. The value of x is:

x = 0.125 * 20 = 2.5

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)