1/2 of Andy's money is 3/5 of Bob's money. If Andy has $15 more than Bob, how much money do they have altogether?

Answer 1

So let us use variables to act as each person's amount of money. A is for Andy's money, while B is for Bob's money. Based on that alone, the equations you can create are as follows: 1/2A = 3/5B and we know that A= B + 15. Or you can put B= A - 15. Either way, you can plug in the second equation into the first one. Therefore, you can end up with 1/2 (B + 15) = 3/5B. If you perform your operations correctly, you will get 1/2B + 7.5 = 3/5B. Now we need to get B by itself, so you can find the least common denominator between 1/2 and 3/5, which is 10. Therefore, you get 5/10B + 7.5 = 6/10B. You can subtract the 5/10B from 6/10B, which gives you 7.5 = 1/10B. To get rid of the 1/10, you can multiple by its reciprocal, which is 10/1. Thus, you have 75 = B. Now we have to find A. Plug in the 75 into the first equation, which gives you 1/2A = 3/5 (75). Do some more math to get 1/2A = 45. Remember, you can multiple by the reciprocal to eliminate the fraction and get A by itself. Therefore, you get 45 x 2 = 90. A is equal to 90. We know that Andy has $15 more dollars than Bob. To check your work, you can plug in A = B + 15. 90 = 75 + 15 is correct.