Question 1152303: A company that manufactures inline skates needs to order three
parts—part A, part B, and part C. For one shipping order the company
needs to buy a total of 6000 parts. There are four times as many B
parts as C parts. The total number of A parts is one-fifth the sum of
the B and C parts. On previous orders, the costs had been $0.25 for
part A, $0.50 for part B, and $0.75 for part C, resulting in a cost of
$3000 for all the parts in one order. When filling out an order for
new parts, the company sees that it now costs $0.60 for part A, $0.40
for part B, and $0.60 for part C. Will the company be able to buy the
same quantity of parts at the same price as before with the new prices?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let a equal the number of A parts.
let b equal the number of B parts.
let c equal the number of C parts.
a + b + c = 6000
on previous orders:
.25a + .5b + .75c = 3000
you were given that:
b = 4c
a = 1/5 * (b + c)
in the second of these equations, replace b with 4c to get:
a = 1/5 * (4c + c)
simplify to get a = 1/5 * 5c
simplify further to get a = c
you have:
a = c
b = 4c
in the equation of .25a + .5b + .75c = 3000, replace a with c and b with 4c to get:
.25a + .5b + .75c = 3000 becomes .25c + .5 * 4c + .75c = 3000
simplify to get:
.25c + 2c + .75c = 3000
simplify further to get:
3c = 3000
solve for c to get:
c = 1000
since a = c, then a = 1000 as well.
since b = 4c, then b = 4000
you have:
a = 1000
b = 4000
c = 4000
in the equation .25a + .5b + .75c = 3000, replace a,b,c with their respective values to get:
.25 * 1000 + .5 * 4000 + .75 * 1000 = 3000
simplify to get:
250 + 2000 + 750 = 3000
combine like terms to get:
3000 = 3000
this confirms the values for a,b,c are good.
the formula for the new parts becomes:
.6a + .4b + .6c = total cost
this becomes:
.6 * 1000 + .4 * 4000 + .6 * 1000 = total cost
solve for total cost to get:
total cost = 600 + 1600 + 600 = 2800
your solution will be that the company will not be able to buy the same quantity of parts at the same price as before with the new prices.
in fact, they will be paying 200 dollars less for the same quantity of parts with the new prices.
that's what i get.
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