If 4, 6, p, 27, q are in continued proportion, find the values of p and q
Understand the Problem
The question states that the numbers 4, 6, p, 27 and q are in continued proportion and asks to find the values of p and q.
Answer
$p = 9$, $q = 81$
Answer for screen readers
$p = 9$ and $q = 81$
Steps to Solve
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Understanding Continued Proportion In continued proportion, the ratio between consecutive terms remains constant. This means: $$ \frac{4}{6} = \frac{6}{p} = \frac{p}{27} = \frac{27}{q} $$
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Finding the value of p We can use the first two ratios to find $p$: $$ \frac{4}{6} = \frac{6}{p} $$ Cross-multiply to get: $$ 4p = 6 \times 6 $$ $$ 4p = 36 $$ $$ p = \frac{36}{4} $$ $$ p = 9 $$
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Finding the value of q Now that we know $p = 9$, we can use the ratio $\frac{p}{27} = \frac{27}{q}$ to find $q$: $$ \frac{9}{27} = \frac{27}{q} $$ Cross-multiply to get: $$ 9q = 27 \times 27 $$ $$ 9q = 729 $$ $$ q = \frac{729}{9} $$ $$ q = 81 $$
$p = 9$ and $q = 81$
More Information
Continued proportion problems involve setting up ratios between consecutive terms. Solving these ratios allows you to find the unknown values.
Tips
A common mistake is to incorrectly set up the ratios in the continued proportion. Ensure that each consecutive pair of terms forms a ratio in the correct order. Another mistake is in the cross-multiplication and simplification steps while solving for p and q.
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