Question

Tom and Rob are brothers who like to make bets about the outcomes of different contests between them. Before the last bet, the ratio of the amount of toms money to the amount of robs money was 4:7. Rob lost the latest competition, and now the ratio of the amount of robs money is 8:3. If rob had $280 before the last competition, how much rob have now that he lost the bet? 

Answer 1

After Rob has lost, he will have 120 dollars. We can work this out by establishing that if Rob had 280 dollars before the final competition, and the ration at the point was 4 to 7, then this means that Tom must have had 4/7 of what Rob had, so x=4/7 * 280, x = 4 x 40, x = 160. This means that Tom had 160 dollars and Rob had 280. Adding this together they have a combined 440 dollars, but the ratio is now 8:3. There are 11 parts to the ration, due to the fact that 8 and 3 is 11, so we need to work out one part of the ratio - 440 divided by 11 equals forty. This means that Tom has 8 multiplied by 40 (320 dollars) and Rob has 40 multiplied by 3, so 120 dollars.