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Off the Cuff

Age 11 to 14 Short Challenge Level:

A long-sleeved shirt has 8 front buttons and 2 cuff buttons.
A short-sleeved shirt has 6 front buttons and no cuff buttons.

The factory which makes 'Slimboy Shirts' uses 10 times as many front buttons as cuff buttons.

What is the ratio of long-sleeved shirts to short-sleeved shirts produced by the factory?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.