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?
I know the discount is exactly the same at $175.00. The discount formula for Company A is X * .25. The formula for Company B is X - 50 * .35. I don't know how to write the equation algebraically. I had something like x - .25x = .35(x-50) . I don't think that is right but I am lost as to where to go next. Any help with relevant work would be much appreciated!
2006-12-26 08:12:14 · 5 answers · asked by pctisaac 2 in Science & Mathematics ➔ Mathematics
you have equated the discounted price and the discount
the equation should be
0.25x=0.35(x-50)
multiplyingby 100
25x=35(x-50
25x=35x-1750
adding -35x
-10x=-1750
dividing by -10
x=175
so at a price of $175 the discounts are the same.
2006-12-26 08:55:56 · answer #1 · answered by raj 7 · 1⤊ 0⤋
Yes, the discount from company A is x*.25 when you buy $x worth of widgets, but that means you pay x*.75
To company B you pay x - (x-50)*.35, and so the cost is the same from each company when .75x = x - .35(x-50), which gives the answer you already have, the discount (and therefore the cost, since the discount comes off the same listed cost from each company) is the same when x = 175.
You asked about equations, but you could do it by using inequalities instead:
Cost B < cost A when
x - .35(x-50) < .75 x
.65x + 17.5 < .75x
17.5 < .1 x
175 < x
Or just use discounts. As I said before, the discount comes off the same cost, so we want
discount B > discount A
(x - 50)*.35 > .25x
.35x -17.5 > .25x
.1x> 17.5 etc
In fact you had pretty much solved it yourself. The only thing wrong is that in the equation you wrote, the left side is the price paid to A and the right side is just the discount for B
2006-12-26 08:26:31 · answer #2 · answered by Hy 7 · 1⤊ 0⤋
I drew a little sketch to help me.
Think of the x axis as the order amount, and the y axis as the discounted price.
A is then a line through (0,0) at a slope of (1-.25) = 0.75 or
Ya = 0.75p
B is a line with with a slope of 1 up to p=50, and then a change in slope to 1-0.35 = 0.65
This is perhaps not the best formulation, it might be better to write and equation for the discount itself and not the discounted price.
2006-12-26 08:28:24 · answer #3 · answered by modulo_function 7 · 1⤊ 0⤋
company A charges .75x
Company B charges 50+(x-50).65
break even is
.75x=50+.65x-32.5
.1x=17.5
x=$175
2006-12-26 09:37:06 · answer #4 · answered by mu_do_in 3 · 1⤊ 0⤋
um according 2 my calculations ur crazy who is gonna now that?
2006-12-26 08:24:43 · answer #5 · answered by fluffy 1 · 0⤊ 3⤋