The sum of three numbers, a, b, and c, is 400. One of the numbers, a, is 40 percent less than the sum of b and c. What is the value of b + c ?
A. 40
B. 60
C. 150
D. 250
Answer:D
The sum of three numbers, a, b, and c, is 400. One of the numbers, a, is 40 percent less than the sum of b and c. What is the value of b + c ?
A. 40 B. 60 C. 150 D. 250
Explanation: DThis is a system of equations question in disguise. First, locate a piece of information in this question that you can work with. "The sum of three numbers, a, b, and c, is 400," seems very straightforward. Write the equation a + b + c = 400. Now the question tells you that "one of the numbers, a, is 40 percent less than the sum of b and c." Translate this piece by piece to get a = (1 - 0.4) (b + c), or a = 0.6(b + c). Distribute the 0.6 to get a = 0.6b + 0.6c. Arrange these variables so they line up with those in the first equation as a - 0.6b - 0.6c = 0. To solve for b + c, stack the equations and multiply the second equation by -1: