Question

Here are a few pairs of positive numbers whose sum is 50.

a. Find the product of each pair of numbers.
b. Find a pair of numbers that have a sum of 50
and will produce the largest possible product.
First
Number
1
2
10
Second
Number
49
48
40
c. Explain how you determined which pair of numbers have the largest
product.
tor ic
Product

Answer 1

a. The product of each pair of numbers is:

1 x 49 = 49

2 x 48 = 96

10 x 40 = 400

b. The pair of numbers that will produce the largest possible product is when the two numbers are equal to half of the sum, which is 25. So the pair of numbers is 25 and 25, and the product is 25 x 25 = 625.

c. We can determine the pair of numbers that have the largest product by using the following reasoning: For any two numbers whose sum is fixed, their product is maximized when the two numbers are as close together as possible. This is because the product of two numbers that are far apart is always smaller than the product of two numbers that are closer together and have the same sum. In this case, the sum is 50, so the two numbers that are closest together and add up to 50 are 25 and 25, which give the largest possible product.