Solving Equations to Find the Value of 'a'

The problem asks us to find the value of 'a' in the given mathematical equation: \( 2945 \div 19 - 11 \times 5 = 29 + a \). To solve this, we need to follow the order of operations, often remembered by acronyms like BODMAS or PEMDAS.

Understanding the Order of Operations

BODMAS stands for:

• Brackets
• Orders (powers and square roots)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

We will apply this order to the left side of the equation first.

Step-by-Step Solution

The equation is \( 2945 \div 19 - 11 \times 5 = 29 + a \).

Step 1: Perform Division and Multiplication

According to BODMAS, we perform division and multiplication before subtraction and addition. We work from left to right for these operations.

First, calculate the division:

\( 2945 \div 19 \)

Let's perform the division:

\( \begin{array}{r} 155 \\ 19\overline{)2945} \\ -\underline{19}\downarrow\phantom{00} \\ 104\downarrow\phantom{0} \\ -\underline{95}\downarrow\phantom{0} \\ 95 \\ -\underline{95} \\ 0 \end{array} \)

So, \( 2945 \div 19 = 155 \).

Next, calculate the multiplication:

\( 11 \times 5 = 55 \)

Step 2: Substitute the results back into the equation

Now the equation becomes:

\( 155 - 55 = 29 + a \)

Step 3: Perform the Subtraction

Calculate the left side of the equation:

\( 155 - 55 = 100 \)

Step 4: Simplify the Equation

The equation is now:

\( 100 = 29 + a \)

Step 5: Solve for 'a'

To find the value of 'a', we need to isolate it on one side of the equation. We can do this by subtracting 29 from both sides of the equation:

\( 100 - 29 = 29 + a - 29 \)

\( 100 - 29 = a \)

\( 71 = a \)

So, the value of 'a' is 71.

Verification

We can verify the answer by substituting \( a = 71 \) back into the original equation:

Left side: \( 2945 \div 19 - 11 \times 5 = 155 - 55 = 100 \)

Right side: \( 29 + a = 29 + 71 = 100 \)

Since the left side equals the right side, our calculated value for 'a' is correct.

The value of a is 71.

Revision Table: Key Concepts

Additional Information: Solving Equations Explained

An equation is a mathematical statement that shows two expressions are equal. The process of solving an equation involves manipulating it to find the value of the unknown variable that makes the statement true.

For a simple linear equation like \( 100 = 29 + a \), the goal is to get the variable 'a' by itself on one side. We do this by performing the inverse operation to what is being done to 'a'. In this case, 29 is being added to 'a'. The inverse operation of addition is subtraction. So, we subtract 29 from both sides to maintain the equality:

\( 100 - 29 = 29 + a - 29 \)

\( 71 = a \)

This principle applies to multiplication (inverse is division) and division (inverse is multiplication) as well when isolating a variable. Always perform the same operation on both sides of the equals sign to keep the equation balanced.