A binary operation Δ is defined by a Δ b = a + 3b + 2. Find (3 Δ 2) Δ 5

1. Analyze the question

We are given a binary operation defined as $a \Delta b = a + 3b + 2$. We need to evaluate the expression $(3 \Delta 2) \Delta 5$. This is a two-step problem where we first solve the operation inside the bracket, then use that result to solve the final operation.

2. Explain the concept

A binary operation is simply a rule that tells you how to combine two numbers. In this case, the rule is: "Take the first number, add three times the second number, and then add 2." We must follow the order of operations (BODMAS) to ensure accuracy.

3. Show the solution

Step 1: Solve the expression inside the bracket $(3 \Delta 2)$ Using the formula $a \Delta b = a + 3b + 2$:

• Here, $a = 3$ and $b = 2$.
• $3 \Delta 2 = 3 + 3(2) + 2$
• $3 \Delta 2 = 3 + 6 + 2$
• $3 \Delta 2 = 11$

Step 2: Solve the final expression $(11 \Delta 5)$ Now, we substitute the result from Step 1 into the original equation:

• Here, $a = 11$ and $b = 5$.
• $11 \Delta 5 = 11 + 3(5) + 2$
• $11 \Delta 5 = 11 + 15 + 2$
• $11 \Delta 5 = 28$

4. Identify the answer

Comparing our result to the given options: A. 35 B. 59 C. 28 D. 87

The correct option is C.

5. Tip

When dealing with binary operations in JAMB, always solve the bracketed part first. If you have multiple operations, treat the result of the first operation as a single number and plug it back into the definition. Don't rush the arithmetic—a simple sign error here is the most common reason students lose marks!