Question

math and graphing tutorial
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.
go to bettys breakables, if the price is below $57.14.
go to bettys breakables, if the price is above $57.14.

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 from 80. $80\times(1 - 0.35)=80\times0.65 = 52$.

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 from 60. $60\times(1 - 0.35)=60\times0.65=39$.

Step5: Determine when 35% off is better than $20$ off

Let the original price be $x$. Set up inequality $x-20>0.65x$. Solve for $x$:
$x - 0.65x>20$, $0.35x>20$, $x>\frac{20}{0.35}\approx57.14$. So 35% off is better when $x > 57.14$.

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: $39$
Go to Betty's Breakables, if the price is above $57.14$.