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.