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A certain number x is multiplied by 5. Another number that is 6 less than x is also multiplied by 5. How much greater is the first product than the second product?

Mathematics

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Step-by-step solution

4 steps

  1. Write the expression for the first product.

    A certain number xx is multiplied by 5.
    First product =5x= 5x

  2. Write the expression for the second product.

    Another number that is 6 less than xx is (x−6)(x-6). This number is also multiplied by 5.
    Second product =5(x−6)= 5(x-6)

  3. Calculate how much the first product is greater than the second product by finding their difference.

    Difference = (First product) - (Second product)

    Difference=5x−5(x−6)\text{Difference} = 5x - 5(x-6)

  4. Simplify the expression.

    5x−5(x−6)=5x−(5x−5×6)5x - 5(x-6) = 5x - (5x - 5 \times 6) =5x−(5x−30)= 5x - (5x - 30) =5x−5x+30= 5x - 5x + 30 =30= 30

    The first product is greater than the second product by 30.

    30\boxed{30}
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