SOLUTION: A local deprtment store is having a sale in which you receive $30 off any purchase over $50. A competing store is offering 30% off all purchases over $50. Write and graph two equa
Algebra ->
Linear-equations
-> SOLUTION: A local deprtment store is having a sale in which you receive $30 off any purchase over $50. A competing store is offering 30% off all purchases over $50. Write and graph two equa
Log On
Question 210910: A local deprtment store is having a sale in which you receive $30 off any purchase over $50. A competing store is offering 30% off all purchases over $50. Write and graph two equations that describe the prices at both stores. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! store A is giving $30 off any purchase >= $50.00
store B is giving 30% off all purchases >= $50.00
-----
let x = amount of purchase over 50 dollars.
let y = total amount paid by customer.
-----
for store A:
-----
y = x + 50 - 30 which becomes:
y = x + 20
-----
for store B:
-----
y = .7*(x+50)
-----
no discount:
-----
y = (x+50)
-----
in the following graph:
the slanted line that crosses the y axis on top of the other slanted lines is the line that represents the purchase price without any discounts.
the slanted line that crosses the y axis in between the top slanted line and the bottom slanted line is the line that represents the purchase price with a 30% discount for all purchases over $50.00
the slanted line that crosses the y axis below the other slanted lines is the line that represents the purchase price with a $30.00 discount on all orders over $50.00
-----
x represents purchase price over $50.00
discount starts at $50.00
y represents the purchase price including any applicable discounts.
-----
when x = 0:
y = $50.00 without a discount.
y = $20.00 with a $30.00 discount.
y = $35.00 with a 30% discount.
-----
when x = $409.00:
y = $459.00 without a discount.
y = $429.00 with a $30.00 discount.
y = $321.30 with a 30% discount.
-----
the larger the purchase price, the better the discount with the 30% off the total purchase price.
-----
the following graph shows the relationships expressed above.
horizontal lines represent the total purchase price at x = $409.00.
vertical line represents x = $409.00
intersection of the horizontal with the vertical lines show the values for y when x = $409.00 for the different discounts shown above.
-----
-----
next graph shows the tradeoff point where 30% discount starts getting better than $30.00 discount.
-----
the point where the 30% discount starts getting better than the $30.00 discount is when the total purchase price over $50.00 equals $50.00
the total purchase price without a discount equals $100.00 as indicated in the second graph below.
the total purchase with a $30.00 discount equals $70.00
the total purchase with a 30% discount equals $70.00
after that the 30% discount provides the most savings as evidenced by the lower total purchase price when x > 50.
the horizontal lines in the second graph below show the $100 purchase price without a discount and a $70 purchase price with either discount. this is at the point where the vertical line shows x to be $50.00
