Question

During a trip to the supermarket, Jim bought the following items: Bread $1.45 Beans $0.88 Toothpaste $2.90 Milk $3.55 Dog food $6.50 The state in which he lives levies a 6% sales tax on all items except food for human beings. What was Jim’s total bill? A 3 lb bag of one brand of cat food costs $3.52. A 6 lb bag of another brand costs $6.80. Which brand is cheaper per pound? One brand of plastic garbage bags costs $8.99 for 45 bags. A second brand costs $7.75 for 32 bags. If you have a savings coupon for $0.25 for the second brand, which brand will be cheaper per bag?

Answer 1

Taxable items $2.90 + $6.50 = $9.40

1) $9.40 × .06 = $0.56 tax

Nontaxable items $1.45 + $0.88 + $3.55 = $5.88

Total $9.40 (taxable items) + $0.56 (tax) + $5.88 (nontaxable items) = $15.84

2) 3 lb bag = $3.52 ÷ 3 = $1.17 per pound

6 lb bag = $6.80 ÷ 6 = $1.13 per pound

The six-pound bag is cheaper per pound.

3) First brand = $8.99 ÷ 45 = .199 or 20 cents per bag

Second brand = ($7.75 – $0.25) ÷ 32 = .234 or 23 cents per bag

Even with the coupon, the first brand is slightly cheaper.

Answer 2

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.