Find two numbers whose product is 20 and whose quotient is 5
Factors of 20:
1 * 20
2 * 10
4 * 5
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Let's assume the two numbers are x and y.
We are given two conditions:
1. The product of the two numbers is 20: xy = 20
2. The quotient (division) of the two numbers is 5: x/y = 5
To find the values of x and y, we can solve these two equations simultaneously.
Rearranging the second equation, we get x = 5y.
Substituting this value of x in the first equation, we have:
5y * y = 20
5y^2 = 20
Dividing both sides by 5, we get:
y^2 = 4
Taking the square root of both sides:
y = ±√4 = ±2
Considering both positive and negative values for y, we get two possibilities:
1. When y = 2,
From the equation x = 5y,
x = 5 * 2 = 10
2. When y = -2,
From the equation x = 5y,
x = 5 * (-2) = -10
Therefore, the two numbers whose product is 20 and whose quotient is 5 are 10 and 2, or -10 and -2.
To find two numbers whose product is 20 and whose quotient is 5, we can set up two equations.
Let's assume the two numbers to be 'x' and 'y'.
The first equation is:
x * y = 20
The second equation is:
x / y = 5
To solve this system of equations, we can use the method of substitution.
Rearrange the second equation to solve for x:
x = 5y
Substitute the value of x in the first equation:
5y * y = 20
Simplify the equation:
5y^2 = 20
Divide both sides by 5:
y^2 = 4
Take the square root of both sides:
y = ±2
Now, substitute the value of y back into the equation for x:
x = 5 * ±2
This gives us two possible pairs of numbers:
Pair 1: x = 10, y = 2
Pair 2: x = -10, y = -2
Therefore, there are two pairs of numbers whose product is 20 and whose quotient is 5: (10, 2) and (-10, -2).