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?

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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:

a + b = 110

a = b + 100

a = b + 100

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:

a + b = 110

a - b = 100 (subtracted b from both sides)

a - b = 100 (subtracted b from both sides)

Now add them so they cancel out b:

2a = 210

Now solve for a:

a = 105 (divide both sides by 2)

Now replace a in original equation:

105 + b = 110

b = 5 (subtract 105 from both sides)

b = 5 (subtract 105 from both sides)

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