# Thread: Can anyone help me?

1. ## Can anyone help me?

A mug is 1/6 full of milk. If 565ml are added, the mug will be full. How much does the mug hold? Can someone help me find the solution?

2. Originally Posted by angelmt
A mug is 1/6 full of milk. If 565ml are added, the mug will be full. How much does the mug hold? Can someone help me find the solution?
Let $\displaystyle M$ represent the amount of milk the mug can hold.

So we can set up the following equation:

$\displaystyle \underbrace{\frac{1}{6}M}_{\text{amount originally in mug}}+\underbrace{565}_{\text{amount added to mug}}=\underbrace{M}_{\text{total amount mug can hold}}$

Now, solving for $\displaystyle M$, we have $\displaystyle 565=\frac{5}{6}M\implies M=\dots$

Can you finish the problem?

3. Hello, angelmt!

I don't suppose you made a sketch . . .

A mug is 1/6 full of milk.
If 565 ml are added, the mug will be full.
How much does the mug hold?
Code:
  -   *-------*   -
:   |       |   :
:   |       |   :
:   |       |   :
:   |  565  |   :
C   |       | (5/6)C
:   |       |   :
:   |       |   :
:   |       |   :
:   * - - - *   -
:   |///////| (1/6)C
-   *-------*   -

Let $\displaystyle C$ = capacity of the mug (in ml).

The bottom $\displaystyle \tfrac{1}{6}C$ is filled with milk.

The top $\displaystyle \tfrac{5}{6}C$ contains 565 ml of milk.

There is our equation: .$\displaystyle \tfrac{5}{6}C \:=\:565$

Now solve for $\displaystyle C$ . . .

4. hello
let $\displaystyle x$ be what you're looking for
$\displaystyle x = \frac{5}{6} +\frac{1}{6}$,when you're mug is full.
at the beginning the mug is $\displaystyle \frac{1}{6}$ full,which means $\displaystyle x$ equal only $\displaystyle \frac{1}{6}$,and when you added $\displaystyle 565 ml$, $\displaystyle x$ is $\displaystyle \frac{1}{6} + 565ml$,that is $\displaystyle 565 = \frac{5}{6} = 5\times\frac{1}{6}$ and so $\displaystyle \frac{1}{6} = \frac{565}{5} =113 ml$.
back to your $\displaystyle x$
$\displaystyle x = 113 + 565 = 678 ml$