Math Problem Statement

Answer

Si las magnitudes A y B son IP, calcula x + y + z.

Solution

To solve this problem:

The magnitudes AA and BB are inversely proportional (IP). This means their product is constant:

AB=constant.A \cdot B = \text{constant}.

Step 1: Write down the relationships from the table.

  • For the first column: 60x=constant60 \cdot x = \text{constant}.
  • For the second column: x215=constantx^2 \cdot 15 = \text{constant}.
  • For the third column: y12=constanty \cdot 12 = \text{constant}.
  • For the fourth column: 6z=constant6 \cdot z = \text{constant}.

Since the constant remains the same for all pairs of AA and BB, we can use these equations to solve for x,y,zx, y, z.


Step 2: Solve for xx, yy, and zz.

  1. From the first column: 60x=x21560=15xx=4.60 \cdot x = x^2 \cdot 15 \quad \Rightarrow \quad 60 = 15x \quad \Rightarrow \quad x = 4.

  2. From the third column: y12=604y12=240y=20.y \cdot 12 = 60 \cdot 4 \quad \Rightarrow \quad y \cdot 12 = 240 \quad \Rightarrow \quad y = 20.

  3. From the fourth column: 6z=6046z=240z=40.6 \cdot z = 60 \cdot 4 \quad \Rightarrow \quad 6z = 240 \quad \Rightarrow \quad z = 40.


Step 3: Calculate x+y+zx + y + z.

x+y+z=4+20+40=64.x + y + z = 4 + 20 + 40 = 64.


Final Answer:

64\boxed{64}

Let me know if you would like detailed explanations or additional clarifications!


Follow-up Questions:

  1. What is the principle behind inverse proportionality?
  2. Can we solve a similar problem if the magnitudes were directly proportional?
  3. What are other real-world examples of inverse proportional relationships?
  4. How would the solution change if one of the values in the table was missing?
  5. Can you graphically represent inverse proportionality for AA and BB?

Tip:

Always check whether relationships in problems like this are direct or inverse proportionality before solving!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Inverse Proportionality
Algebra

Formulas

A · B = constant

Theorems

Inverse Proportionality Principle

Suitable Grade Level

Grades 8-10