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?

Results 1 to 4 of 4

- Jul 9th 2009, 11:31 PM #1

- Joined
- Apr 2009
- Posts
- 15

- Jul 9th 2009, 11:36 PM #2
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?

- Jul 10th 2009, 06:38 AM #3

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,028
- Thanks
- 849

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 $\displaystyle C$ . . .

- Jul 10th 2009, 10:20 AM #4

- Joined
- Jun 2009
- From
- Africa
- Posts
- 641

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 $