# Word Problems - Mixtures 1

Mixture (or solution) problems use equations to relate the amounts (either mass or volume) of each substance used in the mixture. The total amount in a mixture is $$A = x + y$$. Where x and y are the amount of each individual substance. There can be many substance in a mixture. Supose you mix 4 fruits into a fruit salad. The total amount will be $$A = w + x + y + z$$.

To make slime, add $$\frac{1}{4}$$ cup of water, $$\frac{1}{4}$$ cup of borax and $$\frac{1}{8}$$ cup of glue. How many cups of slime does this recipe make?

Mixtures can have quantities in weight or volume. Some examples are shown below:

 $$\text{Weight}$$ $$\text{g, kg, lb, ton, oz}$$ $$\text{Volume}$$ $$\text{mL, L, m^3, cups}$$

When the substances added into the mixture are mixtures themselves, we may be interested in only a certain substance within the mixture. The amount of a specific substance in a mixture is $$a = w \cdot A$$. Where $$a$$ is the amount of the substance, $$w$$ is the weight/volume percentage of the substance in the mixture and $$A$$ is the amount of the mixture.

Rubbing alcohol can contain up to $$70%$$ of pure isopropyl alcohol. In a $$250\;[mL]$$ bottle, how much pure alcohol is in it?

A chemical reaction calls for $$100\;[mL]$$ of $$36%$$ hydrochloric acid but the only solutions available are $$30%$$ and $$90%$$ hydrochloric acid. How much of each are required to make the solution you need?

Try another example here.