Simple Math Problem

Question

A bat and ball cost \$1.10.

The bat costs a dollar more then the ball.

How much does the ball cost?

If this is not the correct place to ask a question like this please tell me and I will remove it :)

The ball costs \$0.05, not \$0.10

Answer 1

Many people come to the quick conclusion that the bat costs a dollar or x = 1.00 so when asked what the ball costs or y = ? they form the equation x + y = 1.10 and plugin 1 for x and solve for y. Giving them that the ball is $0.10.

This is incorrect the bat cost a dolar more so x-1.00 = y, y being the cost of the ball. And to find what the ball or bat costs on its own you have to set up a system of equations like so:

x-1.00 = y
x+y = 1.10

-x+1.00+x+y = 1.10-y
1.00+2y = 1.10
2y = 0.10
y = 0.05

Wether or not the person who is asked this question gets it correct or not depends on if they think you are trying to trick them. If they do think that you are tricking them they will really think about the problem and find the flaw in their original assumption. If not they will quickly answer with the incorrect answer to this simple fourth grade style math problem.

Answer 2

java’s two-variable solution is perfectly fine, but you can also go straight to a single equation in one unknown. If $x$ is the cost of the ball in dollars, then the bat costs $x+1$ dollars, and the two together cost $x+(x+1)=2x+1$ dollars. You know that the total cost is $\$1.10$, so $2x+1=\$1.10$, $2x=\$0.10$, and $x=\$0.05$. It’s entirely a matter of personal preference which approach you take.

Answer 3

Since a ball costs one dollar less than the bat, two ball cost one dollar less than a bat and a ball. Thus two balls cost 10 cents....

Answer 4

I'd like to suggest that the naive guess described at the beginning of java's answer will quickly lead to the correct answer if people would just remember the maxim drilled into us by our elementary-school teachers: Check your answer! If one guesses that the ball costs \$0.10, then checking would lead one to see that the bat costs \$1.10 and therefore the total is \$1.20. Not only does one then see that the answer is wrong, but I think one also sees why it's wrong; the guessed price of the ball has contributed to the price of the bat too, and as a result, the excess over \$1.00 is twice what it should be. So correct for that doubling by halving the guess. I think this approach could be used by people who know no algebra but have good common sense.