BTGModeratorVI wrote: ↑Thu Jul 23, 2020 6:34 am
The sum of three integers A, B and C is 120. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
A. 20
B. 30
C. 45
D. 50
E. 70
Answer:
E
Source: Veritas Prep
The sum of three integers A, B and C is 120
We can write: A + B + C = 120
A is one third of the sum of B and C
We can write: A = (1/3)(B + C)
Multiply both sides by 3 to get:
3A = B + C
B is one fifth of the sum of A and C.
We can write: B = (1/5)(A + C)
Multiply both sides by 5 to get:
5B = A + C
There are MANY different ways to solve this system of 3 equations.
Here's ONE solution.
Take A + B + C = 120 and replace
B + C with
3A to get: A +
3A = 120
Solve to get A = 30
Take A + B + C = 120 and replace
A + C with
5B to get: B +
5B = 120
Solve to get B = 20
Now that we now A = 30, and B = 20, AND we know that A + B + C = 120, we can conclude that C = 70
Answer: E
Cheers,
Brent
