Our Worst Critics Prefer to StayEspecially in light of today's QOTD, the Times never said it better.
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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 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)
Simplifying
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
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