SOLUTION: One number is 5 more than another. Five times the smaller is 2 more than twice the larger. Find the numbers. Bill has twice as much money as bob. Paul has $12 more than Bill.

You can put this solution on YOUR website!
You have three separate problems here -- you should probably ask one problem at a time in the future.


In the first problem we're told that one number is 5 more than another. Let represent the number, then represents the other. Five times the smaller (i.e., ) is 2 more than twice the larger (i.e., ). This produces the equation . Now we just solve for . Expanding the equation produces which simplifies to . Subtracting from both sides produces . Now divide both sides by yields . This means the smaller number is 4 and the other number is 5 more than that; i.e. 4+5, or 9.


For the second problem, let represent the money for Bob. Bill has twice that amount, or . Paul has $12 more than Bill, or . Together they have $92, represented by the equation . We combine like terms to get . Subtracting 12 from both sides yields . Now divide both sides by 5 to produce . That means Bob has $16. Bill has twice that, or $32; Paul has $12 more than Bill, or $44. Adding $16+$32+$44 produces the sum of $92.


For the third problem, let represent one of the numbers. Because the numbers are consecutive, the other number is represented by . Their sum must total 93, represented by the equation . Combining like terms produces . Solving for as in the process above produces . That means the second number is one more than that, or 47. Sure enough, .