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Algebra AMC-8 Math Olympiad

Mixture | Algebra | AMC 8, 2002 | Problem 24

Try this beautiful problem from Algebra based on mixture from AMC-8, 2002.. You may use sequential hints to solve the problem.

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

Mixture | AMC-8, 2002 | Problem 24


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%

Key Concepts


Algebra

Mixture

Percentage

Check the Answer


Answer:40%

AMC-8, 2002 problem 24

Challenges and Thrills in Pre College Mathematics

Try with Hints


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

Can you now finish the problem ……….

Find total mixture

can you finish the problem……..

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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