Question

In a small town, there are 4 times as many left-handed males as there are left-handed females, and there are 3 times as many right-handed females as there are right-handed males. There are a total of 204 males and 348 females in the town. Let x represent the number of left-handed females, and let y represent the number of right-handed males. Write a system of equations to represent the situation. What is the value of x , the number of left-handed females?

A. 4x + 3y = 204 , x = 24
B. 4x + 3y = 348 , x = 6
C. 3x + 4y = 204 , x = 96
D. 3x + 4y = 348 , x = 108

Answer 1

The correct system of equations is 4x + y = 204 and x + 3y = 348, corresponding to answer choice A. Solving the system, we find that x, the number of left-handed females, is 24.

Step-by-step explanation:

Solving the system of equations 4x + y = 204 and x + 3y = 348, we look for the solution that matches one of the answer choices provided. This system corresponds to answer choice A.

Substituting y from the first equation into the second, we find:

4x + y = 204 (1)

x + 3y = 348 (2)

Multiply equation (1) by 3:

12x + 3y = 612 (3)

Now subtract equation (2) from equation (3):

12x + 3y = 612-(x + 3y = 348)

11x = 264

x = 24

Thus, the number of left-handed females, x, is 24.