word problem?

Question

There are two companies that sell widgets. Both companies sell the widgets to the general public for the same price. In order to earn business, Company A offers a special 25% discount on each order. In response, Company B offers a 35% discount on every dollar the customer spends over $50. Both discounts are rounded to the nearest cent. If you place an order for $50 or less, it is less expensive to order from Company A. If you place a large enough order, it will be less expensive to order from Company B. At what price does it become less expensive to order from Company B?
Determine the actual price at which Company B will give you a greater discount than Company A.

1. Explain how you reached this conclusion.

Answer 1

Set it up as an inequality.

Say you need to buy x dollars worth of widgets.

From company A, it'll cost you (0.75)x dollars.

From company B, it'll cost you 50 dollars plus .65 times the rest of x. You can write this as: 50 + (x – 50)(0.65).

Now, you need to find x where 50 + (x – 50)(0.65) is less than (0.75)x. In other words:
50 + (x – 50)(0.65) < (0.75)x

Solving for x gets you:

0.65x + 17.5 < 0.75x
17.5 < 0.10x
175 < x

So, you need more than 175 dollars in your initial order to get a good deal from company B.

Answer 2

Let x = cost of the order
Company A = x - 0.25x
Company B = x - 0.35(x - 50)

Let Company A = Company B and solve the equation for x. At any price above x, Company B will be less expensive.

Answer 3

x is your cost
Company A x - 0.25x
Company B x - 0.35(x - 50)

A = B
x-0.25x = x-0.35(x-50)
Distrubute the -0.35
x-0.25x=x-0.35x+17.5
Combine like terms
-0.35x+-0.35x+17.5
0.10x=17.5
x=175
If x is greater then 175 then Company B will be the better deal.
You can check your work by plugging in 175 into Company A's equation and then into Company B's equation.


Hope this helps you.