Question

The ratio of two numbers is 8:7. The product of these numbers is 896. What is the smaller of these two

Answer 1

Answer:

  28

Step-by-step explanation:

You want the smaller of the two factors of 896 that have the ratio 8:7.

Setup

Let x represent the smaller of the two factors (the one we want to find). Then the larger factor is (8/7)x, and their product is ...

  x(8/7)x = 896

  (8/7)x² = 896

Solution

Multiplying by the inverse of the coefficient of x², we have ...

  x² = (7/8)(896) = 784

  x = √784 = 28 . . . . . . . . take square root

The smaller of the two numbers is 28.

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Additional comment

The larger is (8/7)(28) = 32.