Problem #1 (10 points)

Number problem. One number is two less than another. Use a rational expression to represent the sum of the reciprocals of the two numbers.

Problem #2 (10 points)

Social science. A company is selling a natural insect control that mixes ladybug beetles and praying mantises in the ratio of 7 to 4. If there are a total of 110 insects per package, how many of each type of insect is in a package?

Problem #3 (10 points)

Business and finance. In Bucks County, the property tax rate is $25.32 per $1000 of assessed value. If a house and property have a value of $128,000, find the tax the owner will have to pay.

Problem #4 (10 points)

Science and medicine. The combined resistance of two resistors R1 and R2 in a parallel circuit is given by the formula

Simplify the formula.

Problem #5 (10 points)

Science and medicine. Jan and Tariq took a canoeing trip, traveling 6 mi upstream against a 2 mi/h current. They then returned to the same point downstream. If their entire trip took 4 h, how fast can they paddle in still water? [Hint: If r is their rate (in miles per hour) in still water, their rate upstream is r - 2 and their rate downstream is r + 2.]

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