The difference stays the same, film 1 of 2

Here's the problem. Aaron has three hundred and forty dollars. Bala has two hundred and twenty dollars. They each buy the same pair of sneakers. After they pay, Aaron's money to Bala's money is 8 to 3. How much did the sneakers cost? Try it first. Pause if you like. Draw what we know. One bar for Aaron. Three hundred and forty. One bar for Bala. Two hundred and twenty. Before anything happens, look at the difference between them. Three hundred and forty minus two hundred and twenty is one hundred and twenty. Now they both pay the same price. Watch the difference between the bars. The same price comes off each bar. Both bars get shorter together, so the difference can't change. Still one hundred and twenty. Now the ratio. After paying, Aaron has 8 for every 3 Bala has. 8 equal units to 3. Aaron sticks out by 5 blue units. And that extra piece is exactly the difference. So 5 blue units is the difference. 5 units is one hundred and twenty. Now 1 blue unit. One hundred and twenty divided by 5 is 24. So 1 blue unit is 24 dollars. Bala keeps 3 units. 3 times 24 is 72. Bala started with two hundred and twenty, so two hundred and twenty minus 72 is one hundred and forty eight. The sneakers cost one hundred and forty eight dollars. Both bars went down together. And the difference never changed.