Sure, let's break down Joseph's calculation step by step to find the correct answer and understand where he made a mistake to arrive at 90.
### Part (i): Work out the correct answer
The expression given is:
[tex]\[ 4 + 6^2 - (5 \times 2) \][/tex]
Let's process this step-by-step.
1. First, compute [tex]\(6^2\)[/tex]:
[tex]\[ 6^2 = 36 \][/tex]
2. Next, compute [tex]\(5 \times 2\)[/tex]:
[tex]\[ 5 \times 2 = 10 \][/tex]
3. Substitute the calculated values back into the expression:
[tex]\[ 4 + 36 - 10 \][/tex]
4. Add and subtract in the appropriate order:
[tex]\[ 4 + 36 = 40 \][/tex]
[tex]\[ 40 - 10 = 30 \][/tex]
So, the correct answer is:
[tex]\[ 30 \][/tex]
### Part (ii): Show how Joseph could have got the answer 90
To understand how Joseph might have arrived at the answer 90, let’s explore a possible misinterpretation or mistake in his calculation. Here are the steps:
1. Joseph may have first added 4 to [tex]\(6^2\)[/tex]:
[tex]\[ 4 + 36 = 40 \][/tex]
2. Instead of subtracting [tex]\( (5 \times 2) = 10 \)[/tex] correctly, he might have interpreted the problem differently:
Possibly, he miscalculated the subtraction and addition steps. Let's consider he did:
[tex]\[
4 + 36 - 5 + 2
\][/tex]
3. Perform these steps:
[tex]\[ 4 + 36 = 40 \][/tex]
[tex]\[ 40 - 5 = 35 \][/tex]
[tex]\[ 35 + 2 = 37 \][/tex]
This shows an error, as the intermediate result is still not 90.
4. Let’s find a combination that gives 90:
[tex]\[
(4 + 36) + (10 \times 5 - 2 \times 5)
= 40 + 50 = 90.
\][/tex]
Thus, while it is unclear exactly how Joseph arrived at the number 90, a path revealing significant steps in operation misinterpretation is shown in combined steps.
So, Joseph’s incorrect interpretation might have led him to somehow obtain the final result of 90, by manipulating steps and intermediary calculations.
