Question

the following questions highlight how changes in numbers can be measured in both absolute and relative, or percentage, terms. two stores in a mall are having promotions. the first, annies attic, is offering $20.00 off any purchase. the other, bettys breakables, is offering 35% off any purchase. each store offers a music box at a (non - discounted) price of $80 and a faux ming vase for $60.00, as summarized in the following table. determine the promotional price of each item at each store.

item	original price (dollars)	discount: $20.00 off (dollars)	discount: 35% off (dollars)
a faux ming vase	$60.00	$	$

suppose a friend of yours wants to buy a crystal candlestick. you remember seeing this item at both annies attic and bettys breakables, but you do not remember the price. what advice should you give your friend in this situation?

go to annies attic, $20.00 off is always better than 35% off.

go to bettys breakables, 35% off is always better than $20.00 off.

Explanation:

Step1: Calculate music - box price at Annie's Attic

Subtract $20 from original price. $80 - 20=60$

Step2: Calculate music - box price at Betty's Breakables

Find 35% of 80 and subtract. $80\times(1 - 0.35)=80\times0.65 = 52$

Step3: Calculate vase price at Annie's Attic

Subtract $20 from original price. $60 - 20 = 40$

Step4: Calculate vase price at Betty's Breakables

Find 35% of 60 and subtract. $60\times(1 - 0.35)=60\times0.65=39$

Step5: Analyze advice for candlestick

Let the price of the candlestick be $x$. At Annie's Attic, the price after discount is $x - 20$. At Betty's Breakables, the price after discount is $x\times(1 - 0.35)=0.65x$. Set $x - 20=0.65x$. Solving for $x$ gives $x=\frac{20}{1 - 0.65}=\frac{20}{0.35}\approx57.14$. If $x>57.14$, 35% off is better. If $x < 57.14$, $20 off is better.

Answer:

Music - box at Annie's Attic: $60
Music - box at Betty's Breakables: $52
Vase at Annie's Attic: $40
Vase at Betty's Breakables: $39
Neither "Go to Annie's Attic, $20.00 off is always better than 35% off." nor "Go to Betty's Breakables, 35% off is always better than $20.00 off." is correct. The better - deal depends on the original price of the item. If the original price is more than approximately $57.14, 35% off is better. If it is less than approximately $57.14, $20 off is better.