Bessy and Bob algebra word problem

Bessy has 6 times as much money as Bob. But when each earns $6, Bessy will have 3 times as much money as Bob. How much does each have before and after earning the $6?

Solution

Let x be Bob's money, then Bessy's money is 6x

When Bob earns 6 dollars, his money becomes x + 6

When Bessy earns 6 dollars his money becomes 6x + 6


Now Bessy has 3 times as much money as Bob

so the equation is


6x + 6 = 3 * (x + 6)


6x + 6 = 3x + 18


6x + 6 - 6 = 3x + 18 - 6

6x = 3x + 12

6x - 3x = 3x - 3x + 12

3x = 12

x = 4

Before Bob and Bessy earned 6 dollars, Bob had 4 dollars and Bessy has 6 x 4 = 24

After they both earned 6 dollars, Bob had 10 dollars and and Bessy had 30 dollars.

Indeed 30 is 3 times 10.