Math Problem Statement

Solve the equation y/54 = 2/9 and find the value of y.

Solution

The equation in the image is:

y54=29\frac{y}{54} = \frac{2}{9}

To solve for yy, we can use cross-multiplication. Cross-multiplying the fractions gives:

y×9=2×54y \times 9 = 2 \times 54

This simplifies to:

9y=1089y = 108

Now, divide both sides by 9:

y=1089=12y = \frac{108}{9} = 12

Thus, y=12y = 12.

Would you like any further details or clarification on this? Here are 5 related questions:

  1. What are the steps to cross-multiply two fractions?
  2. Can you solve a similar equation, such as x20=34\frac{x}{20} = \frac{3}{4}?
  3. How do you verify your solution once you've found yy?
  4. How does cross-multiplication work when there are variables in both numerators?
  5. Can this method be used to solve proportion problems in real-life situations?

Tip: Always simplify fractions before solving equations—it can make calculations easier and more accurate.

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Math Problem Analysis

Mathematical Concepts

Proportions
Cross Multiplication
Simplification

Formulas

Cross-multiplication: a/b = c/d implies ad = bc

Theorems

Basic Properties of Proportions

Suitable Grade Level

Grades 6-8