S.O.S. Mathematics CyberBoard

[orgchemus]

I have slept on a waterbed since the 70's. Last year I had to replace the mattress. The waterbed mattress measures 80 inches by 84 inches by 10 inches tall. I filled the matress to capacity with water that I thought was about 96 degrees, but after the bed was filled I found out that the actual temperature was only 70 degrees. It took 3 days for the waterbed heater to warm it up to 96 degrees. I had to sleep on the couch for 3 nights.

One thing that I could have done was drain out part of the water and replace it with 130 degree water. If I had done this, how many gallons of the "colder" water would I have had to drain out of the bed and replace with the 130 degree water, so that the temperature of the bed would have been 96 degrees?

Note: 231 Cubic Inches = 1 Gallon


I am trying to make my own Chex Party Mix and sell at a Fund Raiser for Underpaid College Professors. I would like to create 100 pounds of mix that would have an average cost of $1.90 per pound. I will be using the following ingredients:

Chex Cereal - 70 cents per pound

Planters Peanuts - $4.75 per pound

Roll Gold Pretzels - $3.00 per pound

In my mix, for each pound of peanuts, I would use 2 pounds of Pretzels.

How many pounds of Chex Cereal will I need to use to have 100 pounds of mix with an average cost of $1.90 per pound?

[Denis]

[aswoods]

1st problem:

Let x be the amount of 70° water, and y be the amount of 130° water. Now x+y = the number of gallons in the bed, and the average temperature of x and y must be 96°, so you have two equations in two variables.

[orgchemus]

Denis-

If I solved this correct, should I get the following:

Peanut = 13.87 pounds
Pretzel = 27.74 pounds
Chex Cereal = 58.39 pounds

Is this correct?

Thank You,

Shawn Oberembt

[orgchemus]

Aswoods-

Are you saying that the two equations are as follows:

70x + 130y = 67,200 in3
x + y =96

Is this correct?

Thank You,

Shawn Oberembt

[aswoods]

First, x+y = the number of gallons in the bed (which is not 96)

Heat content of water is same as heat content of mixture:

So secondly, 70x+130y = 96(x+y) = 96*(number of gallons in bed)

giving two equations.

[orgchemus]

Aswood-

Then, I should calculate and get the following:

x+y=67,200 in3
70x+130y=6,451,200 in3

Therefore,

70x+130(67,200-x)=6,451,200

70x+8,736,000-130x=6,451,200

-60x=-2,284800

x=38,080in3 or 164.84 gallons

Is this correct?

Thank You,

Shawn Oberembt

[orgchemus]

Aswood-

I figured it out! Thank you for everything and have a wonderful weekend.

Thank You,

Shawn Oberembt

[aswoods]

That's correct, although the question is asking for y, not x.

[Denis]

[orgchemus]

Denis-

Thank you for your help and have a good weekend.

Shawn Oberembt

[bowery boy]

Let the total volume be V

V = (80 x 84 x 10)/231 gallons = 291 gallons

Let the volume to be replaced be v

The heat to be lost by v is 34v

The heat to be gained by (V – v) is 26(V – v) = 26V – 26v

The heat lost = The heat gained

34v = 26V – 26v

60v = 26V

v = (26/60)V

v = (26/60) x 291 = 126.1 gallons