Algebraic Word Problems

[Sajon1996]

Hi! I am having difficulty setting up word problems in algebra in a number sentence. I never seem to know what x should be, and what the equation should be. Here is an example:

There are 20 kilograms of a solution that is 10% salt. How many kilograms of salt must be added to make a solution that is 25% salt?

Thanks for your help!

Sajon

 

[daon2]

"x" is just a tool to be substituted for an unknown quantity. It doesn't need to be an x, and depending on how you solve the problem, x can be different things.

Here the unknown is the amount of salt that should be added... so:

Let x=the amount of kilograms of salt to be added.

There is already 10% of 20kg = 2kg of salt present. If we add x kilograms of salt, we now have (2+x) kilograms of salt, and a total of (20+x) kilograms of "stuff".

After adding x kilograms of salt the percentage of salt to the entire mixture is (2+x)/(20+x). We want to choose (or find) x so that this percentage is equal to 25%, or 1/4.

So: \(\displaystyle \dfrac{2+x}{20+x} = \dfrac{1}{4}\).

Can you solve for x now?

 

[lookagain]

There are 20 kilograms of a solution that is 10% salt. How many kilograms of salt must be added to make a solution that is 25% salt?

Here is an alternate way:



The pure salt you are adding is 100% strength. \(\displaystyle \ \ \) Let x = the amount of kg of pure salt to be added.
You start with 20 kg, \(\displaystyle \ \)add x kg, \(\displaystyle \ \)and end up with a mixture of \(\displaystyle \ \)(20 + x) kg.




\(\displaystyle \dfrac{\boxed{\ kg \ }}{\boxed{ \ 20}}*\dfrac{\boxed{\ \% \ }}{\boxed{ \ 10}} \ + \ \dfrac{\boxed{\ kg \ }}{\boxed{ \ \ x \ \ }}*\dfrac{\boxed{\ \% \ }}{\boxed{ \ 100}} \ = \ \dfrac{\boxed{\ \ \ kg \ \ \ }}{\boxed{ \ 20 + x}}*\dfrac{\boxed{\ \% \ }}{\boxed{ \ 25}} \)



(20)(10) + (x)(100) = (20 + x)(25) \(\displaystyle \ \ \ \ \ \ \ \)<----- Solve this equation for x. \(\displaystyle \ \ \) That will give the number of kilograms of salt needed to be added.