Thinking of two whole numbers. The product of the two numbers is 28. Their difference is 3. What are the numbers?
surely you can think of two factors of 28.
Do they differ by 3?
To find the two whole numbers, let's assign variables to them. Let's call the first number "x" and the second number "y".
We have two pieces of information: the product of the numbers is 28, and their difference is 3. We can write two equations based on these pieces of information:
Equation 1: x * y = 28 (the product of the numbers is 28)
Equation 2: x - y = 3 (the difference between the numbers is 3)
To solve this system of equations, there are different methods you can use. One approach is to use substitution.
From Equation 2, we can isolate one variable in terms of the other. Let's isolate x:
x = y + 3
Now we can substitute this expression for x into Equation 1:
(y + 3) * y = 28
Expanding the equation, we have:
y^2 + 3y = 28
Rearranging the equation:
y^2 + 3y - 28 = 0
Now we have a quadratic equation in terms of y. We can solve for y by factoring or using the quadratic formula. Factoring the equation, we get:
(y + 7)(y - 4) = 0
This gives us two possible solutions for y:
y + 7 = 0 or y - 4 = 0
Solving each equation for y, we find:
y = -7 or y = 4
Now that we have the values for y, we can substitute them back into Equation 2 to find the corresponding values for x.
When y = -7:
x - (-7) = 3
x + 7 = 3
x = 3 - 7
x = -4
So, when y = -7, x = -4.
When y = 4:
x - 4 = 3
x = 3 + 4
x = 7
So, when y = 4, x = 7.
Therefore, the two whole numbers are -4 and 7.