Question

Maggie bought a total of 30 pounds of three different types 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.

Write a written Systems of Equations consisting of three variables that can be used to determine how many pounds of each fruit Maggie bought?

(There are THREE correct answers)

b = 2 ( g + d )
b + 2g + 3d = 46
30b + 30g + 30d = 1
b + 2g + 3d = 30

b + g + d = 30

b + g + d = 46
2b = g + d

Answer 1

Let b pounds be the weight of bananas, d pounds - weight of dragon fruit and g pounds - weight of guavas Maggie bought.

1) Maggie bought a total of 30 pounds of bananas, guavas and dragon, then

b+d+g=30.

2)

• Bananas cost $1 per pound, then b pounds of bananas cost $b;
• Guavas cost $2 per pound, then g pounds of guavas cost $2g;
• Dragon fruit costs $3 per poundd pounds cost $3d.

In total Maggie spent $46, thus,

b+2g+3d=46.

3) The weight of the bananas (b pounds) that Maggie bought was twice the weight of the guavas (g pounds) and dragon fruit (d pounds) combined. So

b=2(g+d).

The system of equations is

`\left\{\begin{array}{l}b+d+g=30\\b+2g+3d=46\\b=2(d+g)\end{array}\right.`

Answer: equations 1, 2 and 5 are correct