Solving Multi Step Equations Worksheets - Free Printable

Problem Analysis:

The task involves solving a series of arithmetic problems and then using the results to solve a final problem. Let's break it down step by step.

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Step-by-Step Solution:

#### 1. \( 3 \times p = 27 \)
We need to find the value of \( p \):
\[
3 \times p = 27
\]
Divide both sides by 3:
\[
p = \frac{27}{3} = 9
\]
So, \( p = 9 \).

#### 2. \( 35 \div p \)
Substitute \( p = 9 \) into the expression:
\[
35 \div 9 = \frac{35}{9} \approx 3.8889
\]
Since the problem does not specify rounding, we keep it as a fraction or decimal for now:
\[
35 \div 9 = \frac{35}{9}
\]

#### 3. \( 2n + 7 = 63 \)
Solve for \( n \):
\[
2n + 7 = 63
\]
Subtract 7 from both sides:
\[
2n = 63 - 7 = 56
\]
Divide both sides by 2:
\[
n = \frac{56}{2} = 28
\]
So, \( n = 28 \).

#### 4. \( 2a \)
We are not given the value of \( a \), so we cannot solve this directly. However, we will assume it is part of a later calculation.

#### 5. \( 3 \times (20 - 13) \)
Simplify inside the parentheses first:
\[
20 - 13 = 7
\]
Then multiply:
\[
3 \times 7 = 21
\]
So, \( 3 \times (20 - 13) = 21 \).

#### 6. \( 3 \times 7 + 9 \div 3 \)
Perform multiplication and division first:
\[
3 \times 7 = 21
\]
\[
9 \div 3 = 3
\]
Then add:
\[
21 + 3 = 24
\]
So, \( 3 \times 7 + 9 \div 3 = 24 \).

#### 7. \( 3 \times (23 + 6) \)
Simplify inside the parentheses first:
\[
23 + 6 = 29
\]
Then multiply:
\[
3 \times 29 = 87
\]
So, \( 3 \times (23 + 6) = 87 \).

#### 8. \( 7y - 2 \)
We are not given the value of \( y \), so we cannot solve this directly. However, we will assume it is part of a later calculation.

#### 9. \( 4c + 9 \)
We are not given the value of \( c \), so we cannot solve this directly. However, we will assume it is part of a later calculation.

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Final Calculation: Numerical Cipher

The final problem asks us to solve a numerical cipher. Typically, this involves substituting values from previous calculations into a formula or pattern. However, the problem does not explicitly state the cipher or how to use the results. Assuming the cipher involves summing all the solved values, let’s calculate:

- From Step 1: \( p = 9 \)
- From Step 2: \( 35 \div 9 = \frac{35}{9} \approx 3.8889 \)
- From Step 3: \( n = 28 \)
- From Step 5: \( 3 \times (20 - 13) = 21 \)
- From Step 6: \( 3 \times 7 + 9 \div 3 = 24 \)
- From Step 7: \( 3 \times (23 + 6) = 87 \)

Sum these values:
\[
9 + \frac{35}{9} + 28 + 21 + 24 + 87
\]

First, convert \( \frac{35}{9} \) to a decimal:
\[
\frac{35}{9} \approx 3.8889
\]

Now sum:
\[
9 + 3.8889 + 28 + 21 + 24 + 87 = 172.8889
\]

If the cipher requires an integer, round to the nearest whole number:
\[
173
\]

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Final Answer:

\[
\boxed{173}
\]