*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 StayEspecially 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?(via Instapundit)

A. $1.10

B. $0.10

C. $0.05

D. $1.00

E. $0.15

Hint: the answer is not B.

## 2 comments:

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

(*** SPOILER ***)

If

B== price of bat

and

A== price of ball

We have two pieces of info --

The bat + the ball is 110 cents (getting rid of the decimal)

Or:

B+A=110

We also know that:

The bat costs 100 cents more than the ball:

B=A+100

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:

A+100+A=110

or

2*A+100=110

Subtract 100 from both sides:

2*A=10

so

A=5

and

B=105

See? Easy. :o)

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 W12)T = 1.00 + L =Algebraic of W2Substituting the value of T from 2 in 13)(1.00 + L) + L = 1.10Combining terms4)2L + 1.00 = 1.10Subtracting one from each side5)2L=(1.10 - 1.00)Simplifying6)2L=0.10Dividing each side by 27)L=0.05Plugging equation 7) into equation 1)8)T + 0.05 = 1.10Subtracting 0.05 from each side9)T = 1.05Plugging 9) into 1)10)1.05 + L = 1.10Subtract 1.05 from each side11)L = 0.05THEREFORE [from 9) and 11)]:The ball (L) costs $0.05; the bat (T) costs $1.05

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