$\frac{1}{4}=\frac{3}{\square}=\frac{\square}{20}$
Answer (2)
Set up the equation with variables: 4 1 = x 3 = 20 y .
Solve for x : x = 3 × 4 = 12 .
Solve for y : y = 4 20 = 5 .
The values that satisfy the equation are 12 , 5 .
Explanation
Understanding the Problem We are given the equation 4 1 = □ 3 = 20 □ . Our goal is to find the numbers that fit into the squares to make the equation true.
Setting up the Equations Let's call the first unknown number x and the second unknown number y . Then we can rewrite the equation as 4 1 = x 3 = 20 y .
Solving for x First, let's solve for x using the equation 4 1 = x 3 . To do this, we can cross-multiply: 1 ⋅ x = 3 ⋅ 4 , which simplifies to x = 12 .
Solving for y Now, let's solve for y using the equation 4 1 = 20 y . Again, we can cross-multiply: 1 ⋅ 20 = 4 ⋅ y , which simplifies to 20 = 4 y . Dividing both sides by 4, we get y = 4 20 = 5 .
Final Answer So, the equation becomes 4 1 = 12 3 = 20 5 . This confirms that our values for x and y are correct. Therefore, the first square should be filled with 12 and the second square should be filled with 5.
Examples
Imagine you're baking a cake and the recipe calls for 4 1 cup of sugar for each serving. If you want to make 3 servings, you'll need 12 3 cups of sugar, which simplifies to 4 1 cup per serving. Similarly, if you want to make enough cake for 20 people, you'll need 20 5 cups of sugar per serving, which again simplifies to 4 1 cup. This problem demonstrates how proportional relationships are used in everyday situations like cooking and scaling recipes.
To solve the equation 4 1 = □ 3 = 20 □ , we find that the first square equals 12 and the second square equals 5. Therefore, x = 12 and y = 5 satisfy the equation. We confirm that all parts of the equation are equivalent to 4 1 .
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