How to solve a specific algebra II word problem?
Trying to help my little brother do his algebra II homework... problem is I can't exactly remember high school math. (Been a while... ). So, the problem is this:
A circus made $100 when 100 people attended. Men paid $5, Women $2, and Children $0.10. How many men, women, and children attended the circus?
Comments
HINT: Write what you know.
Variables:
m = number of men
w = number of women
c = number of children
Given: Men paid $5
Means: value of men's tickets = 5 * m = 5m
Given: Women $2
Means: value of women's tickets = 2 * w = 2w
Given: Children $0.10
Means: value of children's tickets = 0.10 * c = 0.10c
Given: 100 people attended
Means: m + w + c = 100
Given: a circus made $100
Means: 5m + 2w + 0.10c = 100
You have these equations:
m + w + c = 100
5m + 2w + 0.10c = 100
Hmm... It looks like you left out something because there needs to be 3 equations to solve when you have 3 variables. Do you have something like there are 5 more men than women, the ratio of women to children, or something like that?
Let: M = number of men who attended
W = number of women who attended
C = number of children who attended
In this problem, you have THREE UNKNOWNS: the number of men, the number of women, and the number of children; but only TWO EQUATIONS: one based on the total number of people who attended, and another based on the total revenues; that is,
Equation1: M + W + C = 100
Equation2: 5M + 2W + 0.10C = 100
Equation3: ?
The number of equations should be at least equal to the number of unknowns for you to solve algebra problems. Thus, this problem cannot be solved with accuracy, since it lacks 1 equation. This equation could be an expression of the ratio of men to women and children, or the percentage of women in the crowd, etc.