AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 9 Medium

Two baskets of apples are to be distributed among classes A, B, and C.

Class A receives \frac{2}{5} of the total amount. The remaining apples are divided between classes B and C in a ratio of 5:7. It is known that the weight of the second basket is \frac{9}{10} of the first basket and is 5 kilograms less than the first basket. How many kilograms of apples does class B receive?

  • A.

    33

  • B.

    35

  • C.

    23.75

  • D.

    41

  • E.

    30.25

Answer:C

Class A receives \frac{2}{5} of the total apples, and the remaining amount is divided between classes B and C in a ratio of 5:7.

Then, class B receives: \left(1 - \frac{2}{5} \right) \times \frac{5}{5 + 7} = \frac{1}{4} and class C receives: \left(1 - \frac{2}{5} \right) \times \frac{7}{5 + 7} = \frac{7}{20}

The weight of the first basket is: 5 \div \left(1 - \frac{9}{10} \right) = 50 \quad \text{(kg)}

So the total weight of the two baskets is: 50 + \frac{9}{10} \times 50 = 95 \quad \text{(kg)}

The amount class B receives is: 95 \times \frac{1}{4} = 23.75 \quad \text{(kg)}

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