Which two numbers have a product of 56 and a quotient of 14
56 / x = 14
Multiply both sides by x
Well, if the two numbers have a product of 56 and a quotient of 14, then they must be 7 and 8. That's right, they're like the prodigious duo of multiplication and division!
Let's call the two numbers "x" and "y". We know that the product of these numbers is 56, so we have the equation:
x * y = 56
We also know that the quotient of these numbers is 14, which means dividing one number by the other gives us 14. We can express this in the equation:
x / y = 14
To find the values of x and y, we can solve these two equations simultaneously. We'll rearrange the second equation to solve for x:
x = 14 * y
Now we substitute this expression for x into the first equation:
(14 * y) * y = 56
Simplifying this equation, we get:
14y^2 = 56
Divide both sides of the equation by 14:
y^2 = 4
Taking the square root of both sides, we find:
y = ±2
Now we can substitute the values of y into the expression for x:
If y = 2: x = 14 * 2 = 28
If y = -2: x = 14 * -2 = -28
Therefore, the two numbers that have a product of 56 and a quotient of 14 are 28 and 2, or -28 and -2.
To find two numbers that have a product of 56 and a quotient of 14, we need to use algebra. Let's assume that the two numbers are x and y. We are given two conditions:
1. The product of the two numbers is 56, so we can write the equation: x * y = 56.
2. The quotient of the two numbers is 14, so we can write the equation: x / y = 14.
To find the values of x and y, we can solve these two equations simultaneously.
First, rearrange the second equation to isolate x: x = 14 * y.
Then substitute the value of x in the first equation: 14 * y * y = 56.
Simplify the equation: 14y^2 = 56.
Divide by 14 on both sides: y^2 = 4.
Take the square root of both sides: y = ±2.
So, the possible values for y are 2 and -2.
Substitute each value of y back into the second equation to find the corresponding values of x:
For y = 2, x = 14 * 2 = 28.
For y = -2, x = 14 * -2 = -28.
Therefore, the two numbers that have a product of 56 and a quotient of 14 are 28 and 2, or -28 and -2.