Solve the following problems on your own piece of paper, showing your work in an orderly manner and according to the guidelines for what you must do when "showing your work" summarized below.
a) Write down, in words, precisely what your variable(s) stands for. Then represent other unknown quantities in the problem. (If you wish, you may show this information in a chart, provided that the rows and columns of your chart are clearly labeled.)
b) Write down an appropriate equation(s).
c) Show the steps of solving the equation(s).
d) Use words to answer the question. Your final answer should be stated in an English sentence or phrase. (Exception: In a so-called "number problem," your answer might consist of just a single number.) Your answer should include units when appropriate.
No variable should appear in your final answer. Also, mathematical symbols, such as the equal sign, should not be used in your final answer.
1. Sue has a total of $8,500 split into two investments. Part is invested in a certificate of deposit paying 4.75% per year and the rest is invested in a bond paying 6.65% per year. If the annual interest from the two investments is $512.05, how much money does Sue have invested at each rate?
2. Jim has a part-time job selling newspaper and magazine subscriptions. One week he earns $62.20 by selling 10 newspaper and 6 magazine subscriptions. The following week he earns $79 by selling 12 newspaper and 8 magazine subscriptions. How much does he earn for each newspaper and each magazine subscription he sells?
3. Ted mixed peanut and almond M&Ms to take on a road trip. Peanut M&Ms cost $2.49 a pound and almond M&Ms cost $3.29 per pound. If he ended up with 4 pounds of a mixture that cost $3.00 per pound, how many pounds of each kind of M&M did he use?
4. Pat invested $4,000 of his money in two different stocks. Over one month, his stock in computers earned 17%, but the stock in apples lost 3%. If he had a total of $4,251 after the month, how much money did he invest in each stock?
5. Last year, Sarah was four years older than Amy. In two years, Sarah will be twice as old as Amy. How old are each of them now?