Question

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?

Answer 1

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 `-> a=3b`;
• Sammy has $4 less than Sauder `-> c=a-4`;
• Sammy has $5 more than Sony `-> c=b+5`

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

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

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

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

`a=3b=3*4.5=13.5`
`c=a-4=b+5=13.5-4=4.5+5=9.5`