Three whole numbers, when added two at a time, have sums of 763, 1003,
and 1064. Compute the largest of the original three numbers.
I have no idea how to do this..HELP PLEASE?
Let A,B,C be three numbers, where
A>B>C.
The two larger numbers, A & B, must add up to 1064, or A+B=1064.
The two smaller numbers, B & C, must add up to 763, or B+C=763.
so A+C=1003.
Now you have three equations, can you solve for the three unknowns?
Yes i can.
THe answer is 652.
Thanks.
Perfect! The other two are 412 and 351.
To solve this problem, let's use algebraic approach and assume the three numbers as variables.
Let's call the three numbers A, B, and C.
From the given information, we have the following equations:
A + B = 763 (Equation 1)
B + C = 1003 (Equation 2)
A + C = 1064 (Equation 3)
To find the largest of the original three numbers, we need to find what values of A, B, and C make the equation valid.
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of elimination:
1. Subtract equation 2 from equation 1: (A + B) - (B + C) = 763 - 1003
Simplifying, we get: A - C = -240 (Equation 4)
2. Subtract equation 3 from equation 1: (A + B) - (A + C) = 763 - 1064
Simplifying, we get: B - C = -301 (Equation 5)
Now, we have two equations (Equation 4 and Equation 5) with only two variables A and C. We can solve them simultaneously.
3. Multiply Equation 4 by -1: -A + C = 240 (Equation 6)
4. Add Equation 6 to Equation 5: -A + C + B - C = 240 - 301
Simplifying, we get: -A + B = -61 (Equation 7)
Now, we have two equations (Equation 5 and Equation 7) with only two variables A and B.
5. Add Equation 5 to Equation 7: B - C + -A + B = -301 - 61
Simplifying, we get: 2B - A - C = -362 (Equation 8)
6. Add Equation 5 to Equation 2: B - C + B + C = -301 + 1003
Simplifying, we get: 2B = 702
Dividing both sides by 2, we find B = 351.
Now that we know the value of B, we can substitute it back into Equation 7 to find the value of A:
-A + B = -61
-A + 351 = -61
Subtracting 351 from both sides, we get: -A = -412
Dividing both sides by -1, we find A = 412.
Similarly, we can substitute B = 351 and A = 412 into Equation 2 to find the value of C:
B + C = 1003
351 + C = 1003
Subtracting 351 from both sides, we get: C = 652.
Therefore, the largest of the original three numbers is C, which is 652.