chemistry question: density?

Question

The density of ethylene glycol is 9.35 lbs/gal and water is 62.5 lbs/ft^3.
Assuming the density of water/ethylene glycol is simply the weighted average of the amounts of the two liquids mixed; what is the density in g/cm^3, of a mixture containing 1.00 gallons of ethylene glycol and 3.00 gallons of water?

Please show your work so I can learn how to do this type of problem!! Thanks...

Answer 1

A weighted average is the sum (part/total)(value of part). For example, if we have a collection of people where 25% are 6ft, 50% are 5.8ft, and another 25% are 5ft. The average height of these people is:

(.25(6) + .50(5.8) + .25(5))ft = 5.65ft

Another example is the collection of numbers (3, 3, 3, 3, 4, 4, 4, 5, 5, 6)

There are 10 total numbers, four threes, three fours, two fives and one six. The average of all these numbers is then

(4/10)3 + (3/10)4 + (2/10)5 + (1/10)6 = 4

the density in this case is:

(1/4)62.5lbs/ft^3 + (3/4)9.35lbs/gal

In order to simplify further we need common units;

ft^3=7.48gal

so

((1/4)(62.5/7.48) + (3/4)9.35)lbs/gal

=9.1lbs/gal