Suppose they were all the same

Siti buys 20 pens and erasers. A pen costs 3 dollars and an eraser costs 1 dollar. She pays 44 dollars altogether. How many pens does she buy? Try it first. Pause if you like. Here are her 20 items. We do not know yet which ones are pens. Assume all 20 items are erasers. It is not true, but it gives us a place to start. 20 erasers at 1 dollar each cost 20 times 1, which is 20 dollars. But Siti pays 44 dollars. 44 minus 20 is 24, so she pays 24 dollars more. Change one eraser into a pen. There are still 20 items. But the cost goes up by 3 minus 1, which is 2 dollars. Every change adds 2 dollars. 24 divided by 2 is 12, so 12 erasers change into pens. So Siti buys 12 pens.

There are 18 bicycles and cars in a car park. They have 52 wheels altogether. How many bicycles are there? Try it first. Pause if you like. Here are all 18 of them. Assume all 18 are bicycles. 18 bicycles have 18 times 2, which is 36 wheels. But there are 52 wheels. 52 minus 36 is 16, so there are 16 more wheels. Change one bicycle into a car. There are still 18 of them. But the wheels go up by 4 minus 2, which is 2. Every change adds 2 wheels. 16 divided by 2 is 8, so 8 of them are cars. The question asks for bicycles. 18 minus 8 is 10, so 10 are bicycles. So there are 10 bicycles. Assume they are all one kind, then count the changes that make up the difference.