Question

Maggie bought 30 pounds of produce to feed her hungry hippopotamus. Bananas cost $1 per pound; guavas cost $2 per pound; and dragon fruit costs $3 per pound. Maggie spent $46. The weight of the bananas that Maggie bought was twice the weight of the guavas and dragon fruit combined. Which system of equations in three variables can be used to determine how many pounds of each fruit Maggie bought?

Answer 1

Answer:  Required system:

x+y+z=30

x+2y+3z = 46    

x= 2y+2z      

Step-by-step explanation:

let x=  Number of pounds of bananas

y = Number of pounds of guavas

z = Number of pounds of dragon fruit

According to the question,

x+y+z=30     (i) (total fruits bought = 30 pounds)

Bananas cost $1 per pound; guavas cost $2 per pound; and dragon fruit costs $3 per pound and total cost = $46.

∴ x+2y+3z = 46         (ii)

Also, weight of the bananas= 2 (weight of the guavas+ weight of dragon fruit)

∴ x = 2(y+z)

⇒x= 2y+2z       (iii)

from (i), (ii) and (iii)

x+y+z=30

x+2y+3z = 46    

x= 2y+2z      

are the equations for the required system.