Chairs, Tables, and Ratios

Today I have a very easy question, but once again, two solutions. They are different in their approach, and anyone can choose what works best for him.

The ratio of the price of a table to the price of a chair is 5:3. A table costs $500 more than a chair. How much does each cost?

First, here is one answer (not mine):

Let x be the price of chairs.
That means x + 500 is the price of tables. From the ratio, we can solve the following equation and get each price:
5/3 = (x + 500) / x
5x = 3x + 1500
2x = 1500
x = 750

That makes tables cost $1250. And indeed, when you figure out the ratio, 1250:750 = 25:15 = 5:3.

However, there is another way to answer this question (my way):
Since the ratio is 5:3, you can also call it 5x:3x, where 5x is the price of a table and 3x is the price of a chair. Now we can solve a simpler equation:
5x = 3x + 500
2x = 500
x = 250

Notice that x is not a price of a chair or a table, it's just the unit that gives the price of each. That means the price of a table is $250 * 5 = $1250 and chairs cost $250 * 3 = $750.

This is another way of solving simple math questions using creative thinking.

Hope you liked it,
Nadav

nadavs