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?
6
24
96
108

Answer 1

(b) 24

Explanation:

The given variable definitions and the given relationships let us write these statements:

LH males = 4 × LH females = 4x

RH females = 3 × RH males = 3y

LH males + RH males = 204 = 4x +y

RH females + LH females = 348 = 3y +x

Your favorite method of solving equations of this sort can tell you ...

(x, y) = (24, 108)

There are 24 left-handed females.

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Additional comment

Other numbers involved here are ...

y = 108 . . . . right-handed males

204-108 = 96 . . . . left-handed males (=4×24)

348-24 = 324 . . . . right-handed females (=3×108)

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If you want to solve the equations by hand, you can use substitution for y to get an equation in x:

3(204 -4x) +x = 348 ⇒ -11x = -264 ⇒ x = 24