Solve the following proportion for x and y, rounding your final answers to 1 decimal place

3  :  x  :  11 =  y  :  8  : 7

To solve this proportion for \( x \) and \( y \), let's break down the ratios step by step.

The given proportion is:

\[
3 : x : 11 = y : 8 : 7
\]

This notation implies that the ratios are equal, so:

\[
\frac{3}{y} = \frac{x}{8} = \frac{11}{7}
\]

Let's use each pair of ratios to solve for \( x \) and \( y \).

### Step 1: Solve for \( y \)
Using the ratio \( \frac{3}{y} = \frac{11}{7} \):

1. Set up the equation:
   \[
   \frac{3}{y} = \frac{11}{7}
   \]

2. Cross-multiply to solve for \( y \):
   \[
   3 \cdot 7 = 11 \cdot y
   \]
   \[
   21 = 11y
   \]
   \[
   y = \frac{21}{11} \approx 1.9
   \]

So, \( y \approx 1.9 \).

### Step 2: Solve for \( x \)
Using the ratio \( \frac{x}{8} = \frac{11}{7} \):

1. Set up the equation:
   \[
   \frac{x}{8} = \frac{11}{7}
   \]

2. Cross-multiply to solve for \( x \):
   \[
   x \cdot 7 = 11 \cdot 8
   \]
   \[
   7x = 88
   \]
   \[
   x = \frac{88}{7} \approx 12.6
   \]

So, \( x \approx 12.6 \).

### Final Answer:
- \( x \approx 12.6 \)
- \( y \approx 1.9 \)

Would you like further details or have any questions?

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Here are 5 related questions for further practice:

1. Solve for \( z \) in the proportion \( 5 : z = 10 : 15 \).
2. If \( a : b : c = 4 : 9 : 12 \), and \( a = 8 \), what are the values of \( b \) and \( c \)?
3. Find \( x \) if \( 2 : 6 = x : 18 \).
4. Solve the proportion \( 7 : 5 = x : 20 \).
5. Given \( x : 3 : 9 = 4 : y : 12 \), solve for \( x \) and \( y \).

**Tip:** When solving proportions, cross-multiplication is often the most efficient way to isolate the variable.

Solve the following proportion for x and y, rounding your final answers to 1 decimal place

3 : x : 11 = y : 8 : 7

Learn how to solve the proportion 3 : x : 11 = y : 8 : 7 to find the values of x and y, rounded to one decimal place. This solution covers essential math concepts like ratios, proportions, and cross-multiplication, making it ideal for students in Grades 6-8.

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