Problem |
Solution |
1) Grandpa tells Nelli he has an investment in a fund that has a history of increasing in values by 6.2% every year. He has $32,000 invested in that fund. He asks her to compute how much the fund will earn him over five years if he makes no changes to his investment. Express your answer to the nearest cent.
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Careful! They are asking for the amount he earns, not the total value of his investment after 5 years! The formula for compound interest is:
    A = P (1 + r) t where:
    P is the principal
    r is the interest rate (in decimal)
    t is the number of time periods (in our case, years)
Using P = $32,000, r = 0.062, and t = 5:
A = 32000 (1.062)5
A = $32000 x 1.3509 = $43,228.74
He earns $43,228.74 - $32,000 = $11,228.74
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2) Ben wants to make a lot of crepes. He has 3 cups of milk left and 1 and 1/2 cup of flour. He has plenty of eggs and everything else he needs. The recipe calls for 3/4 cups milk and 3/8 cup flour and yields 6 crepes. What is the maximum number of crepes he can make with the ingredients he has?
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- Compute the number of recipes he can make with his milk
    n = 3 / (3/4) = 3 x (4/3) = 4
- Compute the number of recipes he can make with his flour
    n = 11⁄2 / 3⁄8 = 3⁄2 x 8⁄3 = 4
- So he can make 6 x 4 = 24 crepes.
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3) The numbers 1 - 32 can be represented with a set of five
lights using the binary system. An on light is recorded with a
1, an off light is recorded with a 0. With the pattern given in
the table, how would the number 23 be represented in 1's and
0's?
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This is the binary number system. In this system, each binary digit (bit) is a power of 2, from right to left, so the 32 this problem talks about with 5 'lights' is 25 = 32, the left-most row of this table. All you have to do is make up the number 23 with these powers of 2! Here they are:
  16 (24) +
    4 (22) +
    2 (21) +
    1 (20)
  23 = 0 1 0 1 1 1
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