The product of two numbers is 50. If you divide the larger number by the smaller number
you get 2. What are the numbers?
x*y=50
x/y=2
10*5=50
10/5=2
equation #1 : xy = 50
equation #2 : x/y = 2 ---> x = 2y
sub #2 into #1
2y(y) = 50
y^2 = 25
y = ± 5
if y = 5 then x = 10
if y = -5 then x = -10
to the two numbers are 10,5 OR -10,-5
Let's assign variables to the two numbers. Let's call the larger number "x" and the smaller number "y".
According to the given conditions:
1. The product of the numbers is 50: xy = 50.
2. If you divide the larger number by the smaller number, you get 2: x/y = 2.
To find the values of x and y, we can use algebraic manipulation to solve the system of equations.
From the second equation, we can rearrange it to get y in terms of x: y = x/2.
Substituting this value of y into the first equation, we have:
x * (x/2) = 50.
Simplifying the equation, we get:
x^2/2 = 50.
Multiplying both sides of the equation by 2, we have:
x^2 = 100.
Taking the square root of both sides, we get:
x = sqrt(100).
x can be either 10 or -10, but since we're looking for positive numbers, x = 10.
Substituting this value of x back into the second equation, we have:
10/y = 2.
Solving for y, we get:
y = 10/2 = 5.
Therefore, the two numbers are 10 and 5.