The product of two consecutive multiples of 5 is 500. What are these numbers?

A student asked for the consecutive multiples of 5 whose product is 500. To find these numbers, we would start by considering the properties of multiples of 5. Each multiple will end in either 0 or 5. Since the product is a whole number, we are looking for two integers, where one integer is the next multiple of 5 after the other.
Let's let the first consecutive multiple of 5 be n, making the next consecutive multiple n+5. The product of these two numbers is given by:
n x (n+5) = 500
Solving for n:
n2 + 5n = 500
n2 + 5n - 500 = 0
Factoring the quadratic equation gives us (n+25)(n-20) = 0
So, n = -25 or n = 20
We discard n = -25 as we are looking for positive multiples and accept n = 20.
Therefore, the consecutive multiples are 20 and 25.
These two numbers, 20 and 25, are the consecutive multiples of 5 that result in a product of 500.

Answered by Burger1123 | 2024-06-24

The consecutive multiples of 5 that multiply to 500 are 20 and 25. We find these by setting up the equation n ( n + 5 ) = 500 and solving for n . After factoring and solving the quadratic equation, we determine the multiples are indeed 20 and 25.
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Answered by Burger1123 | 2024-10-15