The following questions highlight how changes in numbers can be measured in both absolute and relative, or percentage, terms.

Question

Two stores in a mall are having promotions. The first, Annie's Attic, is offering $10.00 off any purchase. The other, Betty's Breakables, is offering 40% off any purchase.
Each store offers a music box at a (non-discounted) price of $60 and a faux Ming vase for $30.00, as summarized in the following table.

Determine the promotional price of each item at each store.

Suppose a friend of yours wants to buy a crystal candlestick. You remember seeing this item at both Annie's Attic and Betty's Breakables, but you do not remember the price.
What advice should you give your friend in this situation?
Go to Betty's Breakables, if the price is below $25.00.
Go to Betty's Breakables, if the price is above $25.00.
Go to Annie's Attic, if the price is above $25.00
Go to Betty's Breakables, 40% off is always better than $10.00 off.
Go to Annie's Attic, $10.00 off is always better than 40% off.

Answer 1

Let's first determine the promotional prices for each item at both stores.

1. Calculate Promotional Prices

Annie's Attic (offers $10.00 off):

• Music Box:
  Original Price = $60.00
  Promotional Price = $60.00 - $10.00 = $50.00

• Faux Ming Vase:
  Original Price = $30.00
  Promotional Price = $30.00 - $10.00 = $20.00

Betty's Breakables (offers 40% off):

• Music Box:
  Original Price = $60.00
  Discount = 40% of $60.00 = 0.40 * $60.00 = $24.00
  Promotional Price = $60.00 - $24.00 = $36.00

• Faux Ming Vase:
  Original Price = $30.00
  Discount = 40% of $30.00 = 0.40 * $30.00 = $12.00
  Promotional Price = $30.00 - $12.00 = $18.00

Summary of Promotional Prices:

• Music Box:

  • Annie's Attic: $50.00
  • Betty's Breakables: $36.00

• Faux Ming Vase:

  • Annie's Attic: $20.00
  • Betty's Breakables: $18.00

2. Advice on Buying the Crystal Candlestick:

To determine the best advice for your friend regarding the crystal candlestick purchased from either store, we need to consider the relevance of the discounts offered by each store.

• If the price of the item is below $25.00, the 40% off from Betty's Breakables would yield greater savings compared to the $10 off from Annie's Attic. For example:

  • If the original price = $25.00, then 40% off = $10 off, the same as Annie's. If it’s lower (say $24.00), 40% would provide a discount of $9.60 (leaving a promotional price of $14.40), better than Annie's.

• If the price is above $25.00, we have to check:

  • If the original price is $30.00 (the price of the faux Ming vase), then 40% is $12, and you'll pay $18, which is better than Annie's price of $20.

Given the consistent discount provided by Betty's Breakables (40% off), which is a proportional discount, it generally tends to yield better or similar outcomes for items priced above $25.00.

Thus, the safest recommendation would be:

• Go to Betty's Breakables, 40% off is always better than $10.00 off.

This is because for most prices above $25.00, a 40% off discount would provide a better deal compared to a flat $10 discount.