Anna buys bananas, grapes, and apples. she buys twice the amount of bananas as grapes. she buys 2 more pounds of apples than grapes. altogether, anna bought 14 pounds of fruit. how many pounds of each fruit did she buy?

Let the amount of grapes be g. The amount of grapes, bananas, and apples are represented as follows.

Grapes: g
Bananas: 2g
Apples: g + 2

The total amount is 14; that means the above expressions must be equal to 14. Set up an equation and solve algebraically for g.

14 = g + 2g + (g + 2)
14 = g + 2g + g + 2
14 = 4g + 2
12 = 4g
3 = g

Remember, g represents the amount of grapes; that means Anna bought 3 pounds of grapes. To find the amount of bananas and apples, substitute into the expressions 2g and g + 2.

2g  =>  2(3)  =>  6
g + 2  =>  3 + 2  =>  5

Anna bought 3 pounds of grapes, 6 pounds of bananas, and 5 pounds of apples.