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Try this beautiful problem from Algebra based on Mixture from AMC-8, 2002.

Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki uses her juicer to extract 8 ounces of pear juice from 3 pears and 8 ounces of orange juice from 2 oranges. She makes a pear-orange juice blend from an equal number of pears and oranges. What percent of the blend is pear juice?

- 34%
- 40%
- 26%

Algebra

Mixture

Percentage

But try the problem first...

Answer:40%

Source

Suggested Reading

AMC-8, 2002 problem 24

Challenges and Thrills in Pre College Mathematics

First hint

Find the amount of juice that a pear and a orange can gives...

Can you now finish the problem ..........

Second Hint

Find total mixture

can you finish the problem........

Final Step

3 pear gives 8 ounces of juice .

A pear gives \(\frac {8}{3}\) ounces of juice per pear

2 orange gives 8 ounces of juice per orange

An orange gives \(\frac {8}{2}\)=4 ounces of juice per orange.

Therefore the total mixer =\({\frac{8}{3}+4}\)

If She makes a pear-orange juice blend from an equal number of pears and oranges then percent of the blend is pear juice= \(\frac{\frac{8}{3}}{\frac{8}{3}+4} \times 100 =40\)

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- https://www.youtube.com/watch?v=lHgyrwyZcpw

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