Question

In the last election, candidate C received 15,000 fewer votes than candidate B. If a total of 109,000 votes were cast, how many votes did candidate B receive?

The price of gourmet coffee beans at the corner market has increased 10% per year over the past several years. If the current cost is $14 per pound, what did a pound of gourmet coffee beans cost two years ago?

Gage bought a new car for $29,000 to use while he is away at college. The car depreciates (decreases in value) by 11% annually. If he plans to sell the car once he graduates in four years, what will the value of the car be?

Ms. B and Ms. D are writing problems for an algebra book. Ms. B started with ten problems already written, and she can write six problems an hour. Ms. D had no problems written, but she writes ten problems an hour. When will Ms. D have the same number of problems written as Ms. B? How many problems will they each have written at that time?

Answer 1

1.) Let C be the votes gathered by candidate C, and B be the votes gathered by candidate B. The equation would be:

C = B - 15,000      -----> eqn 1
B + C = 109,000   -----> eqn 2

Substituting eqn 1 to eqn 2:
B + (B - 15,000) = 109,000
Solving for B,
B = 62,000 votes

2.) The general formula would be

 Projected Cost = Base Cost (1+ 0.1t), where t is time in years
 $14 = x(1+0.1*2)
 x = $11.67

3.) The general formula would be

 Future Worth = Present Worth (1 -  0.11t), where t is time in years
 Future Worth = $29,000(1-0.11*4)
 Future Worth = $16,240

4a.) You have to equate the number of problems written by Ms. B and Ms.D.
        
        Ms. B = Ms. D
        10+6t = 10t, where t is the number of hours
         Solving for t,
         t = 2.5 hours

4b.) Using the time in #4a, the number of problems is equal for Ms. B and Ms. D because we equated the two expressions. Any of those could be used.

     10 + 6t = 10 + 6(2.5) = 25 words