... the participants took a three-question math test with questions such as, "A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?"
The intuitive answer to that question is 10 cents, since most people's first impulse is to knock $1 off the total. But people who use "reflective" reasoning to question their first impulse are more likely to get the correct answer: 5 cents.
My mathematical ineptness is legendary, but I've always been pretty good at arithmetic. So what am I missing here? What accounts for the remaining 5 cents? Also, it may well be that there is no one-size-fits-all way to arrive at truth.
The ball costs 5 cents. The bat costs one dollar more than that---so, $1.05. Add 'em together, and you get $1.10.ReplyDelete
If you're a dullard like some of us and not good at guessing or at just seeing the answer, a little algebra helps:ReplyDelete
x is the cost of the ball
(1.00 + x) is the cost of the bat
(1.00 + x) + x = 1.10
1.00 + 2x = 1.10
1.00 + 2x - 1.00 = 1.10 - 1.00
2x = .10
2x/2 = .10/2
x = .05
1.00 + x = 1.00 + .05 = 1.05
1.05 + .05 = 1.10
What about taxes?ReplyDelete
They were purchased in New Hampshire, which has no sales tax.ReplyDelete