Two numbers have a product of 676 and a quotient of 4.
What are the numbers?
xy = 676 and x/y = 4
from the second we get x = 4y
put that back into the first and solve for y.
I am sure you can take it from here.
Let's solve this step by step.
Step 1: Let's assume the two numbers are "x" and "y".
Step 2: According to the information given, we can write two equations:
Equation 1: x * y = 676
Equation 2: x / y = 4
Step 3: We can solve Equation 2 for x in terms of y. Multiplying both sides by y gives us:
x = 4y
Step 4: Substitute the value of x from Equation 3 into Equation 1:
(4y) * y = 676
Step 5: Simplify the equation:
4y^2 = 676
Step 6: Divide both sides of the equation by 4:
y^2 = 169
Step 7: Take the square root of both sides:
y = +/- 13
Step 8: Now we have two possible values for y. Substituting back into Equation 2, we can find the corresponding values for x:
If y = 13:
x = 4 * 13 = 52
If y = -13:
x = 4 * (-13) = -52
Step 9: So, the two numbers are 52 and -52.
Therefore, the two numbers with a product of 676 and a quotient of 4 are 52 and -52.
To find the two numbers, let's assign variables and write equations.
Let's call the two numbers x and y.
We know that their product is 676, so we can write the equation:
x * y = 676
We also know that their quotient is 4, which means x divided by y equals 4. So we can write another equation:
x / y = 4
To solve this system of equations, we can use substitution or elimination. Let's use substitution.
Rearrange the second equation to solve for x:
x = 4y
Now substitute this value of x into the first equation:
4y * y = 676
Multiply:
4y^2 = 676
Divide both sides by 4:
y^2 = 169
Take the square root of both sides:
y = ±13
Since we're looking for two numbers, let's consider both the positive and negative square roots for y: y = 13 and y = -13.
Now substitute these values of y back into the second equation to find x:
x / 13 = 4 or x / -13 = 4
Cross-multiply:
x = 52 or x = -52
So, the possible pairs of numbers are (52, 13) and (-52, -13).