GoldenLeaf

Wow, I must have been really sleepy... expanding, not factoring. It was already factored >.<

...

Spare me some change?

Factoring!

(2x+4)(x-4)

First

Inner

Outer

Last

2x*x

2x*-4

4*x

4*-4

2x^2

-8x

4x

-16

Combine like terms

4x - 8x = -4x

And line them all up.

2x^2 - 4x - 16 is your final answer.

Thanks CPhill :D

More number-crunching. This time, it's gonna be two parts 70% solution and one part 40% solution. This one is really easy to figure out the numbers for, but just for you:

$${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{30}}\right) = {\mathtt{10}}$$

10 liters of 40% solution were used.

Same as the last one, crunch numbers until you get a ratio. In this case, it will be two parts 40% solution and one part 10% solution.

$${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{10}}\right) = {\frac{{\mathtt{10}}}{{\mathtt{3}}}} = {\mathtt{3.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

So 3.333... liters of 10% solution were used.

For this problem, we need to get to a 50% ratio first, and go from there. To do this, we have to combine 70% and 10% and then take the average of those to see if it reaches 50%.

The way I found it was just to test every combination, and eventually I found a mixture of two parts 70% solution and one part 10% solution gave us 3 parts of a 50% solution. So now that we have our ratios, we can solve.

$${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{15}}\right) = {\mathtt{5}}$$

So 5 liters of 10% solution was used.

$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{15}}\right) = {\mathtt{10}}$$

And 10 liters of 70% solution was used.

So, if you have a 30% salt solution and a 40% salt solution, then combining an equal amount of a 30 and a 40 would result in a 35.

$${\frac{\left({\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\mathtt{40}}\right)}{{\mathtt{2}}}} = {\mathtt{35}}$$

So, the 30% and 40% solutions would be in equal parts to each other.

If there are 100 liters of a 35% solution and the solutins used to make the new solution were 30% and 40%, then, because it would be equal parts, there would be 50 liters of 40% solution used.

Yep, got it right zegroes!

Set up a ratio.

$${\frac{{\mathtt{3.5}}}{{\mathtt{1\,000}}}} = {\frac{{\mathtt{x}}}{{\mathtt{300\,000}}}}$$

Do the Butterfly method to make the equation easier.

$${\mathtt{3.5}}{\mathtt{\,\times\,}}\left({\mathtt{300\,000}}\right) = {\mathtt{1\,000}}{\mathtt{\,\times\,}}{\mathtt{x}}$$

Divide by 1000 on both sides to get x alone.

$${\frac{\left({\mathtt{3.5}}{\mathtt{\,\times\,}}{\mathtt{300\,000}}\right)}{{\mathtt{1\,000}}}} = {\mathtt{x}} \Rightarrow {\mathtt{x}} = {\mathtt{1\,050}}$$

You would get $1050