At first, the ratio of dave's savings to sam's savings was 5: 4. after each of them donated $40 to charity, the ratio of dave's savings to sam's savings became 13: 10. what was dave's savings at first?

$300

Step-by-step explanation:

Let Dave's saving be D and Sam's savings be S

"At first, the ratio of Dave's savings to Sam's savings was 5:4":

"After each of them donated $40 to charity, the ratio of Dave's savings to Sam's savings became 13:10":

So we subtract 40 from each of them and then the ratio becomes 13 is to 10. Hence we can write:

Plugging in into S (as we found earlier), we can solve for D (our answer):

So, Dave's savings at first, D, is $300.

ANSWER

Dave's savings at first was $300

EXPLANATION

Let the total savings of Dave and Sam be



Since their savings is in the ratio,



The total ratio



Dave's Savings at first is



and Sam's savings at first is



When each of them donate $40 each, then

Dave's savings is now


or



and Sam's savings is now



Or



The ratio of their savings is now



We can now write the proportion,


This implies that,



This simplifies to,



We cross multiply to get,



We expand to get,



We group like terms to get,



This simplifies to,



We divide through by -2, to get,



Dave's savings at first is,







Therefore Dave's savings at first was $300

The solution to the system of equations (-2,2)