# Sauder has three times as much money as Sony. Sammy has $4 less than Sauder and$5 more than Sony. How much money does each have?

Oct 14, 2015

Sauder has $13.5$$, Sony has 4.5$$, Sammy has $9.5.

#### Explanation:

Why they all have names with the same letters! :P Anyway, let's call Sauder $a$, Sony $b$ and Sammy $c$. Translating into equation, we have

• Sauder has three times as much money as Sony $\to a = 3 b$;
• Sammy has $4 less than Sauder $\to c = a - 4$; • Sammy has$5 more than Sony $\to c = b + 5$

And let's solve the system. Given the first equation, we can substitute $a$ with $3 b$. By doing so, second and third equations become

$c = 3 b - 4$
$c = b + 5$

Since both $3 b - 4$ and $b + 5$ equal to $c$, they must be equal to each other, so we have $3 b - 4 = b + 5$, and solving for $b$ we get $2 b = 9$, and thus $b = \frac{9}{2} = 4.5$.

Now that we know $b$, we can easily find $a$ and $c$:

$a = 3 b = 3 \cdot 4.5 = 13.5$
$c = a - 4 = b + 5 = 13.5 - 4 = 4.5 + 5 = 9.5$