Math Problem Statement

Solve the equation: (2 × ☐) / (3 × ☐) = 8 / ☐

Solution

The problem in the image appears to be a fraction equation with missing values:

2×3×=8\frac{2 \times \square}{3 \times \square} = \frac{8}{\square}

Here’s how to solve for the missing numbers step-by-step:


Step 1: Represent the equation

Let the missing boxes be variables:

  • The first box in the numerator is aa.
  • The first box in the denominator is bb.
  • The box in the denominator of 8\frac{8}{\square} is cc.

The equation becomes:

2×a3×b=8c\frac{2 \times a}{3 \times b} = \frac{8}{c}


Step 2: Cross-multiply

Cross-multiplying gives:

(2×a)×c=(8)×(3×b)(2 \times a) \times c = (8) \times (3 \times b)

Simplify:

2ac=24b2ac = 24b


Step 3: Solve for specific variables

Without further information, the problem could have multiple solutions depending on the values of aa, bb, and cc. Often in such problems, one set of values (e.g., integers) satisfies the equation. Let’s test the most likely simple solution:

  1. Assign a=4a = 4: Then 2×a=82 \times a = 8, so the numerator matches the right-hand side.

  2. Assign b=1b = 1: Then 3×b=33 \times b = 3, keeping the denominator balanced.

  3. Solve for cc: Substituting a=4a = 4 and b=1b = 1 into 2ac=24b2ac = 24b:

    2(4)c=24(1)2(4)c = 24(1) 8c=248c = 24 c=3c = 3


Final Solution:

The missing numbers are:

  • a=4a = 4
  • b=1b = 1
  • c=3c = 3

Would you like me to explain any step in more detail or verify this solution further? Let me know!


Related Questions:

  1. How can cross-multiplication be used to solve fraction equations?
  2. What are the rules for solving equations with multiple variables?
  3. How do proportional relationships work in math?
  4. Can this problem have other solutions? How would you find them?
  5. What are the real-world applications of solving such equations?

Tip:

When solving equations with fractions, always start by cross-multiplying to eliminate the fractions for easier calculations!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Proportions
Cross-multiplication

Formulas

Cross-multiplication: (a/b = c/d) => a × d = b × c
Fraction simplification

Theorems

Basic principles of fractions and proportionality

Suitable Grade Level

Grades 6-8