twenty times the square of a non-zero number is equal to 15 times the number. what is the number?
Let's assume the number is represented by "x".
The given equation can be written as:
20x^2 = 15x
To find the value of x, we can simplify the equation by dividing both sides by "x":
20x^2 / x = 15x / x
This simplifies to:
20x = 15
Now, we can isolate x by dividing both sides by 20:
20x / 20 = 15 / 20
This simplifies to:
x = 15 / 20
Reducing the fraction:
x = 3 / 4
Therefore, the number is 3/4.
To find the number, let's break down the information given.
The problem states that "twenty times the square of a non-zero number is equal to 15 times the number." Let's represent the unknown number as "x."
According to the problem, we can set up the equation:
20x^2 = 15x
Now, we have a quadratic equation. To solve it, we can rearrange the equation and set it equal to zero:
20x^2 - 15x = 0
Now, we can factor out the common term:
5x(4x - 3) = 0
According to the zero-product property, if a product equals zero, then at least one of the factors must equal zero. So, we can find the value of x by making each factor equal to zero:
5x = 0 or 4x - 3 = 0
The first equation gives us x = 0. However, since the problem states the number should be non-zero, we disregard this solution.
Now, let's solve the second equation:
4x - 3 = 0
Add 3 to both sides:
4x = 3
Divide both sides by 4:
x = 3/4
Therefore, the non-zero number that satisfies the given condition is x = 3/4.
20x^2 = 15x
20x^2 - 15x = 0
5x(4x-3) = 0
so x=0 or x=3/4, but x wan non-zero so
x = 3/4
check:
20(9/16) = 45/4
15(3/4) = 45/4 , yup!