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.

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