Bonus Puzzle #21 Help.?

Question

1) The I.Q of a Martian Varies directly with the square of the number of tentacles it has. If a Martian with 5 tentacles has an I.Q of 75, what it the I.Q of a Martian with 8 tentacles?

2) The 4th term of a sequence is 4 and the 6th term is 6. Every term after the 2nd is the sum of the 2 preceding terms. What is the 8th term of this sequence?

3) At the bank, Al exchanged a $10 for an equal number of nickels, dime, and quarters. How many of each type of coin did Al recieve?

4) What are the teo values of x which satisfy 2/x + x/2= 3/x + x/3 ?

Answer 1

1) Any direct relationship can be expressed as y = kx, where k is a constant. In this case, IQ = y and # of tentacles = x.

IQ = k(# of tentacles)

You're given that an alien with # of tentacles = 5 has IQ = 75, so you can find k:

75 = k(5)

Divide both sides by 5:

k = 15

Then plug in # of tentacles = 8:

IQ = 15(8) = 120

2) The problem says that each term after 2 is the sum of the 2 terms before it.

So the 6th term, a6, is the sum of the 4th (a4) and the 5th (a5):

a6 = a4 + a5

a6 is given as 6, and a4 as 4:

6 = 4 + a5

So:

2 = a5

Now we can find a7:

a7 = a5 + a6 = 2 + 6 = 8

And then a8 is the 8th term, which is what we're looking for:

a8 = a6 + a7 = 6 + 8 = 14

3) Since you have the same number of coins of each type, everything's an x. 10 cents times x + 5 cents times x + 25 cents times x has to add up to $10.

$10.00 = $0.10 x + $0.05 x + $0.25 x = $0.40 x

Divide both sides by $0.40:

x = $10.00/$0.40 = 25

So you'd have 25 of each coin.

Checking:

25($0.05) + 25($0.10) + 25($0.25) = $1.25 + $2.50 + $6.25 = $10.00, check!

4) The original equation is: 2/x + x/2= 3/x + x/3

Multiply both sides by x, which cancels all the x's in the denominator, and squares the ones in the numerator:

2 + 1/2 x² = 3 + 1/3 x²

Subtract 1/3 x² and 2 from both sides:

1/6x² = 1

Multiply through by 6:

x² = 6

Take the positive and negative square root:

x = ±√6

Might as well check:

2/√6 + √6/2 = 3/√6 + √6/3
2/√6 - 3/√6 = √6/3 - √6/2
-1/√6 = (2√6 - 3√6)/6 = -√6/6
-1/√6 (√6/√6) = -√6/6 = -√6/6....check.