Expert: Sherry Wallin - 9/14/2011

Question
1. The gauge of an oil tank indicated that it was 1/7 full. After 240 gallons were added, the gauge indicated that the tanks was now 4/7 full. How many gallons does the tank hold? (Assuming that the gauge is accurate)

2.   There are 190 mg of sodium in 27.0 g serving of Wheaties. Every morning, Hector makes a 75.0g serving of Wheaties. How much sodium does Hector intake with his breakfast each day?

3   Marine biologists capture, tag, and release 137 Florida manatees into a protected region. Several months later, of 90 captured manatees, 6 have tags. Estimate the population of Florida manatees in the protected region.

I was unsure how many questions we are allowed to ask.

Answer
michaelyn~

basically you have a tank that is 1/7 full and when you put some fuel in, exactly 240 gal you now have 4/7 of a full tank. So by adding 3/7 of a tank that was equivalent to 240 gallons. Let x = size of oil tank, (3/7)x = 240 => [(3/7)/(3/7)]x = 240/(3/7) => 7(240)/3 =7(80) => x = 560
The oil tank holds 560 gallons.

Compare mg of sodium to g of Wheaties: 190/27 = x/75 and solve for x

Let x = population.  So they catch 137 and tag them and you have a ratio of sample/pop.  Now you have 6 in a sample and 90 in a pop for 6/90 = 1/15
Set the ratios equal to each other and solve for x: 137/x = 1/15=> x =  15(137) =>2055

There are approximately 2,055 mantees in the protected region.
Math Prof