3 girls whose ages total 36. Sue is 1/3 Jill's age. Sue is 4 times as old as Jane. What are their individual ages?
sue = s
Jill = 3 s
Jane = (1/4) s
so
s + 3 s + s/4 = 36
4 s + s/4 = 36
16 s + s = 144
17 s = 144
s = 144/17
Jill = 3 s = 432/17
Jane = s/4 = 36/17
To solve this problem, we can break it down into steps and assign variables for each girl's age.
Let's represent Sue's age as "s," Jill's age as "j," and Jane's age as "n."
We are given three pieces of information:
1. "Three girls whose ages total 36": This means s + j + n = 36.
2. "Sue is 1/3 Jill's age": We know that Sue's age (s) is equal to 1/3 of Jill's age (j), which can be represented as s = (1/3)j.
3. "Sue is 4 times as old as Jane": Sue's age (s) is also stated as being four times Jane's age (n), written as s = 4n.
Now, let's substitute the values from the second and third pieces of information into the first equation to solve for the ages:
s + j + n = 36
Substitute s = (1/3)j and s = 4n into the equation:
(1/3)j + j + 4n = 36
Multiply the entire equation by 3 to eliminate the fraction:
j + 3j + 12n = 108
Combine like terms:
4j + 12n = 108
Divide the equation by 4:
j + 3n = 27
Now, we have two equations:
1. j + 3n = 27
2. s = 4n
To find the individual ages, we need to solve these two equations simultaneously. However, there is another equation that we can derive from the fact that Sue, Jill, and Jane's ages sum to 36:
s + j + n = 36
Substitute s = 4n into the equation:
4n + j + n = 36
Combine like terms:
5n + j = 36
This equation can be rewritten as:
j = 36 - 5n
Now, we can substitute this expression for j into the equation j + 3n = 27:
(36 - 5n) + 3n = 27
Simplify:
36 - 2n = 27
Subtract 36 from both sides:
-2n = -9
Divide both sides by -2:
n = 4.5
Now that we have the value of n, we can substitute it into j = 36 - 5n:
j = 36 - 5(4.5) = 36 - 22.5 = 13.5
Finally, we can substitute the values of n and j into s = 4n:
s = 4(4.5) = 18
Therefore, Sue is 18 years old, Jill is 13.5 years old, and Jane is 4.5 years old.