Which pair of numbers, whose sum is 35, have the largest product?
To find the pair of numbers with the largest product, given that their sum is 35, we can use a simple algebraic approach.
Let's assume the two numbers are x and y, such that x + y = 35. We are trying to find the values of x and y that maximize the product xy.
To solve this problem, we can rewrite one of the variables in terms of the other. Let's rewrite y in terms of x:
y = 35 - x
Substituting this expression for y back into the equation xy, we have:
P = x(35 - x)
Now, we want to find the maximum value of P, which represents the product. To do this, we can take the derivative of P with respect to x, set it equal to zero, and solve for x:
dP/dx = 35 - 2x
Setting dP/dx equal to zero gives:
35 - 2x = 0
2x = 35
x = 17.5
Since x represents one of the numbers, it cannot be a decimal. So, we can round it up to 18 to get a whole number.
Now we can substitute this value of x back into the equation y = 35 - x to find the value of y:
y = 35 - 18
y = 17
Therefore, the pair of numbers with a sum of 35 and the largest product is 18 and 17.
1+34 product 34...no
2+33 product 66...no
3+32 prodcut 96...no
keep on going
or faster skip a couple of numbers
10+25
15+20
and so on
even faster start from the middle