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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?

Respuesta :

Let the initial savings at first be = x

Given ratio is [tex]\frac{5}{4}[/tex] and after donating $40 to charity, the ratio becomes [tex]\frac{13}{10}[/tex]

Hence, the relation becomes:

[tex]\frac{5x-40}{4x-40}=\frac{13}{10}[/tex]

[tex]10(5x-40)=13(4x-40)[/tex]

= [tex]50x-400=52x-520[/tex]

[tex]-2x=-120[/tex] or

[tex]2x=120[/tex]

[tex]x=60[/tex]

So , Dave's saving at first was 5x = 5*60 = $300

and Sam's saving at first was 4x = 4*60= $240

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