The product of two numbers, A and B is 840. THe difference of two numbers, A and C is 816. GIven that C is the greatest number and B is the smallest 2-digit even number, find the values of A, B, and C?
B=10
So, A=84
So, C=900
Let's solve this step-by-step:
Step 1: Find the factors of 840.
The factors of 840 are: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840.
Step 2: Find the factors that are two-digit even numbers.
From the list above, we can see that the two-digit even factors are 12, 20, 24, 28, 40, 42, 56, 60, 70, 84, and 120.
Step 3: Determine the values of B.
Since B is the smallest two-digit even number, B can be 12.
Step 4: Find the numbers that can yield a difference of 816.
The numbers that can yield a difference of 816 are 828 and 12, 840 and 24, 852 and 36, etc.
Step 5: Determine the values of C.
Since C is the greatest number, C can be 852.
Step 6: Find the value of A.
Since the product of A and B is 840, A can be calculated by dividing 840 by B.
So, A = 840 / 12 = 70.
Therefore, the values of A, B, and C are A = 70, B = 12, and C = 852.
To find the values of A, B, and C, we can use a system of equations based on the given information.
Let's start by assigning variables to the unknown values:
A: First number
B: Smallest 2-digit even number
C: Greatest number
From the problem, we know two things:
1) The product of A and B is 840.
2) The difference of A and C is 816.
Let's write these equations:
Equation 1: A * B = 840
Equation 2: A - C = 816
Now we can solve the system of equations.
Since B is the smallest 2-digit even number, we can list the possible values for B: 10, 12, 14, 16, 18, 20, 22, ...D
We can see that the only 2-digit even number among these is 10.
Substituting B = 10, we have:
A * 10 = 840
Dividing both sides by 10, we get:
A = 840 / 10
A = 84
Now we can substitute the value of A into Equation 2 and solve for C:
84 - C = 816
Subtracting 84 from both sides, we get:
-C = 816 - 84
-C = 732
Since we know C is the greatest number, it cannot be negative. So we need to switch the signs:
C = -732
Therefore, the values of A, B, and C are:
A = 84
B = 10
C = -732