Question

If 893 x 78 = p, which of the following is equal to 893 × 79?

• A. p + 1
• B. p + 78
• C. p + 79
• D. p + 893
• E. p + 894

Hint:

Don't be confused by category labels like "Geometry" if the problem content is clearly algebraic. Focus on the mathematical relationships presented in the question itself. Recognize that increasing one factor in a multiplication by 1 increases the total product by the other factor.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem tests the understanding of the distributive property of multiplication over addition. We are asked to express a new product in terms of a given product, \(p\). Although the heading mentions Geometry, the problem is algebraic in nature.
Step 2: Key Formula or Approach:
The distributive property is key here: \(a \times (b + c) = (a \times b) + (a \times c)\).
Step 3: Detailed Explanation:
We start with the given information:
\[ 893 \times 78 = p \] Our goal is to find an expression for \(893 \times 79\) using \(p\).
We can express 79 as the sum of 78 and 1: \(79 = 78 + 1\).
Let's substitute this into the expression we want to solve:
\[ 893 \times 79 = 893 \times (78 + 1) \] Now, we apply the distributive property to expand the expression:
\[ 893 \times (78 + 1) = (893 \times 78) + (893 \times 1) \] From the problem statement, we know that \(893 \times 78\) is equal to \(p\). Also, \(893 \times 1\) is simply 893.
By substituting these values, we get:
\[ p + 893 \] Thus, \(893 \times 79\) is equivalent to \(p + 893\).
Step 4: Final Answer:
The correct expression is \(p + 893\).