Hattie purchased 12a pounds of apples and 4b pounds of bananas from the grocery store. She then used 2b pounds of bananas and 7a pounds of apples making pies. If a is the cost per apple and b is the cost per banana, which expression represents the total amount Hattie spent?

We know that Hattie purchased 12*a pounds of apples.

We also know that a is the cost per apple, and in one apple we have about 0.33 lb, then in a pound of apples we have N apples, such that:

N*0.33lb = 1lb

N = 1/0.33lb = 3

In a pound of apples, we have 3 apples, then in 12*a pounds of apples we have a total of:

12*a*3 apples.

each apple costs a, then the total cost in apples is:

(12*a)*(3*a)

36*a^2

We also know that she bought 4*b pounds of bananas, and each banana costs b.

We know that one banana weights around the same as an apple, then we also would have 3 bananas in one pound of bananas.

In 4*b pounds of bananas, we wil have:

4*b*3 bananas in total.

And each one costs b, then the price in bananas is:

4*b*3*b

12*b^2

The total cost is:

36*a^2 + 12*b^2