Word problem.

• Mar 14th 2007, 03:28 PM
Ash
Word problem.
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?
• Mar 14th 2007, 05:13 PM
ThePerfectHacker
Quote:

Originally Posted by Ash
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.

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.
• Mar 14th 2007, 09:08 PM
CaptainBlack
Quote:

Originally Posted by Ash
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?

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
• Mar 15th 2007, 04:31 AM
Soroban
Hello, Ash!

There are a number of approaches ... none are straight-forward.
Here's another one . . .

Quote:

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