Find the discount and unit price

Question

(https://i.stack.imgur.com/TP4KX.jpg) One of my tutees ask me this question, and I toyed with it but thought there might be a short cut. Any insight? Trick? Thanks.

Answer 1

It's mostly just looking at what unit prices are reasonable.

1. The original price per ounce is $2.6 / 64 \approx .0765,$ so the discounted price can only be $2.5$ cents per ounce. That means the price paid was $64 \times .025= 1.60,$ so coupon C was used.

2. The original unit price was $4/8 = .5$ per pint, so $45$ cents per ounce looks reasonable, and coupon B achieves this.

3. The original unit price is $8.25 / 6 = 1.375,$ so we guess $1.1$ as the unit price, and since this clearly isn't $50$ percent off, we try coupon A, and sure enough, $1.375 \times .8=1.10.$

4. Now we have only coupon D and a unit price of $33$ cents left, and I leave it up to you to confirm that that works.