Together, Larry and Lenny have $\$$35. Larry has two-fifths of Lenny's amount. How many more dollars than Larry does Lenny have?
I want to find the difference between Lenny's and Larry's amounts. I can use algebra to represent the situation with equations. Let x be the amount that Lenny has. Then Larry has two-fifths of x, which is (2/5)x. The sum of their amounts is 35, so I can write an equation: x + (2/5)x = 35. I can simplify this equation by multiplying both sides by 5 to get rid of the fraction: 5x + 2x = 175. Combining like terms, I get 7x = 175. Dividing both sides by 7, I get x = 25. This means that Lenny has $\$$25 and Larry has (2/5)x, which is (2/5)(25) = 10. The difference between their amounts is 25 - 10 = 15. Therefore, Lenny has $\$$15 more than Larry. 