Final Answer:
The reason you cannot have a figure with exactly 100 counters using the equation n = 3f + 3 is that the figure number that would correspond to 100 counters is not a whole number, which is a requirement for a figure number.
Step-by-step explanation:
Let's use the equation n = 3f + 3, where n is the number of counters and f is the figure number, to explore why it is not possible to have a figure with exactly 100 counters.
Step 1: Set n to 100, since we want to find out if we can have a figure with exactly 100 counters.
Step 2: Plug n = 100 into the equation n = 3f + 3:
100 = 3f + 3
Step 3: Solve for f. To do this, we'll first isolate f on one side of the equation:
100 - 3 = 3f
97 = 3f
Step 4: Divide both sides by 3 to solve for f:
97/3 = f
Step 5: Evaluate the division:
f = 32 1/3
Now, we have our answer for f: it is 32 1/3, which is not an integer but a fraction.
In the context of figures and counters, the figure number f must be a whole number because you cannot have a fraction of a figure.
Since 32 and 1/3 is not a whole number, we cannot have a figure number that corresponds to exactly 100 counters following the given equation.
Therefore, the reason you cannot have a figure with exactly 100 counters using the equation n = 3f + 3 is that the figure number that would correspond to 100 counters is not a whole number, which is a requirement for a figure number.