Sunday, March 02, 2008

Put it On the Money

Early last month, the NY Times' Freakonomics blog solicited suggestions for a six-word U.S. motto.1 Ultimately, readers voted among the best five entries. The winner was announced Thursday:
Our Worst Critics Prefer to Stay
Especially in light of today's QOTD, the Times never said it better.
1 I'm not a big fan of the Levitt/Dubner book Freakonomics (too cute; too many errors), but Stephen Dubner's math problem is both cute and correct:
A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?

A. $1.10
B. $0.10
C. $0.05
D. $1.00
E. $0.15

Hint: the answer is not B.
(via Instapundit)


OBloodyHell said...

For those of you who want to understand how to derive the answer, it is basic Algebra --

(*** SPOILER ***)

B== price of bat
A== price of ball

We have two pieces of info --
The bat + the ball is 110 cents (getting rid of the decimal)

We also know that:
The bat costs 100 cents more than the ball:

Now, the thing to realize is "equals" means "we can substitute it anywhere it appears" ---
so we can replace "A+100" for B anywhere it appears (there are some exceptions involving division, but they don't count here, rather obviously), so:

Subtract 100 from both sides:

See? Easy. :o)

Carl said...

OBH: I think your proof was more efficient than mine. I went to public schools, and was taught thusly:

W1) A bat and a ball cost $1.10 in total.

W2) The bat costs $1.00 more than the ball.

Q) How much does the ball cost?

Variables: Let L be bat; B be ball.

1) T + L = 1.10 = Algebraic of W1

2) T = 1.00 + L = Algebraic of W2

Substituting the value of T from 2 in 1

3) (1.00 + L) + L = 1.10

Combining terms

4) 2L + 1.00 = 1.10

Subtracting one from each side

5) 2L=(1.10 - 1.00)


6) 2L=0.10

Dividing each side by 2

7) L=0.05

Plugging equation 7) into equation 1)

8) T + 0.05 = 1.10

Subtracting 0.05 from each side

9) T = 1.05

Plugging 9) into 1)

10) 1.05 + L = 1.10

Subtract 1.05 from each side

11) L = 0.05

THEREFORE [from 9) and 11)]:

The ball (L) costs $0.05; the bat (T) costs $1.05