Two positive integers aer in the ratio 2:5. If the product of the two integers is 40, find the larger integer.
2x*5x = 40
So, find x, and then 5x.
To solve this problem, we can set up a system of equations. Let's call the two positive integers "x" and "y," with x being the smaller integer and y being the larger integer.
Given that the ratio of x to y is 2:5, we can write the equation:
x/y = 2/5
We are also given that the product of the two integers is 40, so we can write another equation:
x * y = 40
Now we have a system of two equations:
x/y = 2/5
x * y = 40
To solve this system, we can use the equation x/y = 2/5 to find an expression for x in terms of y, and then substitute it into the second equation.
Rearranging the first equation, we have:
x = (2/5)y
Substituting this expression for x in the second equation, we get:
(2/5)y * y = 40
(2/5)y^2 = 40
To further simplify, we multiply both sides of the equation by 5/2:
y^2 = 40 * (5/2)
y^2 = 100
Taking the square root of both sides, we find:
y = √100
y = 10
Now that we have the value of y, we can substitute it back into the expression for x to find x:
x = (2/5)*10
x = 4
So, the larger integer is 10.