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Solve the proportion: 6/54=p/8.
a. p=4
b. p=12
c. p=5
d. p=8

1 Answer

4 votes

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.

User WiseGuyEh
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