Question

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?

Answer 1

Answer:

$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":

$\frac{D}{S}=\frac{5}{4}\\4D=5S\\\frac{4}{5}D=S$

• "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:

$\frac{D-40}{S-40}=\frac{13}{10}\\10(D-40)=13(S-40)\\10D-400=13S-520\\-400+520=13S-10D\\120=13S-10D$

Plugging in $\frac{4}{5}D$ into S (as we found earlier), we can solve for D (our answer):

$120=13S-10D\\120=13(\frac{4}{5}D)-10D\\120=\frac{52}{5}D-10D\\120=\frac{2}{5}D\\D=\frac{120}{\frac{2}{5}}=120*\frac{5}{2}=300$

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

Answer 2

ANSWER

Dave's savings at first was $300


EXPLANATION

Let the total savings of Dave and Sam be

$x \: dollars$


Since their savings is in the ratio,

$5:4$

The total ratio

$= 5 + 4 = 9$


Dave's Savings at first is

$= \frac{5}{9} (x)$

and Sam's savings at first is

$= \frac{4}{9} (x)$


When each of them donate $40 each, then


Dave's savings is now

$= \frac{5x}{9} - 40$
or

$= \frac{5x - 360}{9}$


and Sam's savings is now

$= \frac{4x}{9} - 40$

Or

$= \frac{4x - 360}{9}$


The ratio of their savings is now

$13 : 10$


We can now write the proportion,
$\frac{5x - 360}{9} : \frac{4x - 360}{9} = 13: 10$

This implies that,

$\frac{ \frac{5x - 360}{9} }{ \frac{4x - 360}{9} } = \frac{13}{10}$


This simplifies to,

$\frac{5x - 360}{4x - 360} = \frac{13}{10}$


We cross multiply to get,

$10(5x - 360) = 13(4x - 360)$

We expand to get,

$50x - 3600 = 52x - 4680$


We group like terms to get,


$50x - 52x = - 4680 + 3600$

This simplifies to,

$- 2x = - 1080$

We divide through by -2, to get,

$x = 540$

Dave's savings at first is,

$= \frac{5}{9} \times 540$

$= 5 \times 60$

$= 300$

Therefore Dave's savings at first was $300