Here is the problem.

A set X is partitioned into subsets x1, x2, and x3. The number of elements in x1 is 4 times the number in x2. And the number in x3 is 5 times the number in x2. If n(x)=150, find n(x1), n(x2), and n(x3).

So I have been trouble finding anything online for this since I don't know what this process is called. I tried dividing 150 by many numbers with no success in getting the correct answer. Thanks in advance for your help!

  • 1
    $\begingroup$ Do you know how to solve systems of equations using substitution? Like when you have two equations with two unknowns or three equations with three unknowns? $\endgroup$ Jan 21 '15 at 5:18
  • 1
    $\begingroup$ Apart from the partition terminology, we have $3$ dogs A, B, and C. The weight of A is $4$ times the weight of B, and the weight of C is $5$ times the weight of B. Together they weigh $150$ pounds. How much does each dog weigh? $\endgroup$ Jan 21 '15 at 5:30

Number of elements in $X_i$ is $n(X_i)$.

We know that $$n(X) = n(x_1) + n(x_2) + n(x_3) = 150$$ $$n(x_1) = 4 n(x_2)$$ and $$ n(x_3) = 5 n(x_2).$$

This system of equations can be solved by substituting $n(x_1)$ and $n(x_3)$ to the first equation.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.