Final answer:
After cross multiplying the given proportion and simplifying the fractions, we concluded that none of the provided multiple-choice answers is the correct solution for the variable p. It seems there may be an error in the options provided for this proportion question.
Step-by-step explanation:
To solve the proportion given by 6/54 = p/8, we begin by setting up the equality and then cross multiplying to solve for p.
Cross multiplication yields the following equation:
6 × 8 = 54 × p
This simplifies to:
48 = 54p
Now, we divide both sides of the equation by 54 to isolate p:
p = 48 / 54
Simplifying the fraction on the right-hand side gives us:
p = 4 / 9
However, since we need p to be a whole number and knowing that 4/9 is not a valid answer for this multiple-choice question, we must recheck our calculations. After reevaluation, it becomes apparent that the correct calculation should be:
6 × 8 = 54 × p
48 = 54p
To find p, divide 48 by 54:
p = 48 / 54
Upon reevaluating, we can see that 48 divided by 54 is indeed 8/9 which is not one of the multiple-choice answers provided. After reviewing our steps and the original proportion, we realized that there was an error in the first step as we should have simplified the fraction 6/54 before cross-multiplying.
First simplify 6/54:
6/54 = 1/9 (since 6 divides 54 nine times)
Now we have the proportion:
1/9 = p/8
Cross multiply to solve for p:
1 × 8 = 9 × p
8 = 9p
Divide by 9 to solve for p:
p = 8 / 9
p = 0.888 ≈ 1 (when rounded to the nearest whole number)
But 1 is not an option in the multiple-choice answers either. Considering all given choices, we realize that the solution appears to be missing or incorrect. None of the provided options (a) p=4, (b) p=12, (c) p=5, or (d) p=8 is the solution to this proportion based on our calculations.