Given
1) human food items purchased: (bread, $1.45), (beans, $0.88), (milk, $3.55)
items purchased that were not human food: (toothpaste, $2.90), (dog food, $6.50)
6% sales tax is levied on anything not human food.
2) Cat food costs 3 lb for $3.52 or 6 lb for $6.80
3) Garbage bags cost $8.99 for 45 bags or $7.75 less $0.25 for 32 bags
Find
1) the total bill
2) the size that is cheaper per pound
3) the brand that is cheaper per bag
Solution
1) 6% tax causes the price to be multiplied by 1 + 0.06 = 1.06. Then the bill will be ...
... (total for food items) + 1.06×(total for non-food items)
... $1.45 + 0.88 + 3.55 + 1.06×($2.90 +6.50)
... = $5.88 +1.06×9.40
... = $5.88 +9.96 = $15.84 . . . . total bill
2) The cost of 6 lb of the first brand would be ...
... 6 lb = 2×(3 lb) ⇒ 2×$3.52 = $7.04
This is more than the $6.80 cost of the larger-size bag.
The larger bag (6 lb for $6.80) is the cheaper size/brand.
3) The cost per bag for the first brand is
... cost/bag = $8.99/(45 bags) = $0.19978/bag
The cost per bag for the second brand (with coupon) is
... cost/bag = ($7.75 -0.25)/(32 bags) = $7.50/(32 bags) = 0.23438/bag
The first brand ($8.99 for 45 bags) is cheaper per bag.
_____
The coupon for the second brand would need to be for $1.36 savings in order to match the per-bag price of the first brand.
