Let's assume the two positive numbers are x and y.
According to the problem, the difference between the two numbers is 28. This can be expressed as:
x - y = 28 (Equation 1)
The problem also states that the product of the two numbers is 3900. This can be expressed as:
xy = 3900 (Equation 2)
Now, we can solve this system of equations to find the values of x and y.
From Equation 1, we can isolate x by adding y to both sides of the equation:
x = y + 28 (Equation 3)
Substituting Equation 3 into Equation 2, we get:
(y + 28)y = 3900
y^2 + 28y = 3900
Rearranging this equation to the standard quadratic form, we have:
y^2 + 28y - 3900 = 0
We can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. In this case, we will use factoring:
(y + 78)(y - 50) = 0
Setting each factor equal to zero, we get two possible solutions for y:
y + 78 = 0 --> y = -78 (not a valid solution since we are looking for positive numbers)
y - 50 = 0 --> y = 50
Now that we have the value of y, we can substitute it back into Equation 3 to find the value of x:
x = y + 28
x = 50 + 28
x = 78
Therefore, the two positive numbers that satisfy the conditions are 78 and 50.
Find two positive numbers whose difference is 28
and whose product is 3900
.
1 answer