An Article in The Economist (“Free Exchange”, December 6, 2014) quotes the following problem as an illustration that some of the “underlying assumptions of classical economics” about people’s behavior are incorrect and “the mind plays tricks.” A bat and a ball cost $1.10 between them. the bat costs $1 more than the ball. How much does each cost? Answer this quickly with no writing, then construct a system of linear equations and solve the problem carefully.
Firstly, I beleive that this question was incorrectly stated in the text. The original article (here) contains an additional constraint (in bold above) which gives the problem a bit more meat.
As stated in the article, my brain intuitively and immediately spits out $1 for the bat, and $0.10 for the ball, which i’m pretty sure is incorrect. Let’s take a look:
\[\begin{aligned} (1 + x) + x = 1.10 \\ 1 + 2x = 1.10 \\ 2x = 1.10 -1 \\ 2x = 0.10 \\ x = 0.05 \\ \end{aligned}\]
Above we see that, somewhat as epected, the answer is not the one immediately presented by intuition, but infact $1.05 for the bat and $0.05 for the ball.