Marta went to the farmer's market to buy oranges. the oranges that are 3 inches in diameter cost 25 cents per dozen. the oranges that are 4 inches in diameter are 50 cents per dozen. marta chose the 3-inch oranges. did she make the more economical decision? explain your answer?

no

Step-by-step explanation:

If we consider the volume of each orange ( we have considered the orange as a perfect sphere)

we have the volume=(4/3) * π R^3 where is the orange radius

for 3 inch diameter de volume is =1.33*3.1415*3.37 inch^3

for 4 inch diameter de volume is =1.33*3.1415*8 inch^3

Taking into account a dozen of oranges we have to multiplier by 12 both orange volume are:

V dozen 3-inch= 40.44 inch^3 (paying 25 cent)

V dozen 4-inch= 96.00 inch^3 (paying 50 cent)

If she want to buy more that one dozen is economical  better choose  the 4 inch oranges

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)