Consider the expression 5 × 4 + 20. If the symbols "+" and "×" are interchanged and at the same time the numbers 4 and 5 are also interchanged throughout the expression, which of the following equations shows the correct new value of the expression after these interchanges?

Introduction / Context:
This question involves a structured transformation applied to a simple arithmetic expression. We are told that the symbols "+" and "×" are interchanged and the numbers 4 and 5 are interchanged throughout the expression. The task is to determine the correct numerical result of the transformed expression and match it with the given equation options.

Given Data / Assumptions:

• Original expression: 5 × 4 + 20.
• Every "+" becomes "×" and every "×" becomes "+".
• Every 4 becomes 5 and every 5 becomes 4.
• The transformation is applied only to the left-hand side expression 5 × 4 + 20.
• We then evaluate the new expression using the usual order of operations.

Concept / Approach:
We first interpret the rules carefully to avoid double counting any substitution. The natural reading is: start from the original expression 5 × 4 + 20, systematically interchange the indicated symbols and numbers, and then compute the resulting value. The correct option is the equation whose right-hand side equals this transformed value.

Step-by-Step Solution:
Start with 5 × 4 + 20.Interchange the symbols "+" and "×". The expression becomes 5 + 4 × 20.Now interchange the numbers 4 and 5. The 5 becomes 4 and the 4 becomes 5, giving 4 + 5 × 20.Apply order of operations: first compute 5 × 20 = 100 and then add 4. So the value is 4 + 100 = 104.

Verification / Alternative check:
We can verify by redoing the two substitution steps in a different mental order. If we first interchange 4 and 5, we get 4 × 5 + 20. Then interchanging "+" and "×" yields 4 + 5 × 20, which is the same final expression as before.Evaluating again gives 4 + 100 = 104, so the transformed expression is consistent and independent of the order in which we apply the two types of interchanges.

Why Other Options Are Wrong:
The equation 5 × 4 + 20 = 40 corresponds to treating the original expression without any transformation, since 5 × 4 + 20 = 40.The options with right-hand sides 85 or 95 come from incorrect partial substitutions or wrong arithmetic, but they do not match the correct transformed value of 104.

Common Pitfalls:
A common mistake is to change only the symbols or only the numbers, instead of applying both sets of transformations.Another pitfall is to ignore operator precedence and evaluate 4 + 5 × 20 as (4 + 5) × 20, which would lead to an incorrect result of 180.

Final Answer:
The transformed expression evaluates to 104, so the correct equation is 5 x 4 + 20 = 104.