How would I setup and answer this word problem?
Two parts of pea gravel worth $10.00 per ton are mixed with one part of sand worth $8.00 per ton to form a base for road paving. If the bill for a project is $728.00, what is the approximate price per ton for the mixture?
I assume that the thing (whatever is it) is divided into two equal tons. One is work 10 and one is 8.Originally Posted by Ash
Intotal we have, (if x is amount for half-amount).
10x+8x=728
18x=728
x=40.44
Then the full amount is 2x (because we considered half-amount).
2x=80.88 tons
The average amount being paid is:
PRICE/QUANTITY.
The price is 728 and the Quantity is 80.88
Thus,
728/80.88=9.000
Thus it is 9 dollars.
Let x tons be the total quantity, then there is 2x/3 tons of pea gravel, and x/3 tons
of sand. So total cost is:
10*(2x/3) + 8*(x/3) = 728 dollars.
or:
x*28 = 728*3,
x = 728*3/28 = 78 tons.
Therefor average price of mixture is total price divided by total quantity, which
in this case is: 728/78 = 9.33 dollars per ton
(actually 9 and 1/3 dollars per ton).
RonL
Hello, Ash!
There are a number of approaches ... none are straight-forward.
Here's another one . . .
Two parts of pea gravel worth $10/ton are mixed with one part of sand worth $8/ton
to form a base for road paving. .If the bill for a project is $728.00,
what is the approximate price per ton for the mixture?
Let x = number of tons of sand.
. . At $8/ton, its cost is: 8x dollars.
Let 2x = number of tons of pea gravel.
. . At $10/ton, its cost is: 10(2x) = 20x dollars.
The total cost Is $728: .8x + 20x .= .728 . → . x = 26
Hence, there is 26 tons of sand and 52 tons of pea gravel,
. . a total of 78 tons of "stuff".
The cost per ton is: .$728 ÷ 78 .= .$28/3 .≈ .$9.33
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