Bat and Ball Puzzle

A bat and ball cost a dollar and ten cents.

The bat costs a dollar more than the ball.

How much does the ball cost?

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

If you said 10 cents you are wrong. The ball costs 5 cents.

You can prove this if you use algebra and replace a and b for bat and ball:

The question does not tell you how much either item costs, only the difference between them and their sum.

You have two equations that you can solve with a simultaneous equation:

First rewrite the equations:

Now add them so they cancel out b:

Now solve for a:

Now replace a in original equation: