Name: Product of Two or Three Fractions
Uploaded: 2019-07-19
Duration: 4 min 4 s
Description: If the length and breadth of a rectangle are a fraction, then what is the area of that rectangle? Let’s learn to multiply two or more fractions and find the...

Question

\frac{3}{11}

of the people in a restaurant are adults. If there are

75

more children than adults, find how many adults and how many children are there in the restaurant.

Accepted Answer

Let the total number of people in the restaurant be $k$ .

Given, $\frac{3}{11}$ of the people in the restaurant are adults. So, the number of adults in the restaurant is $\frac{3}{11} k$ .

Hence, the number of children in the restaurant is $k - \frac{3}{11} k = \frac{11 k - 3 k}{11} = \frac{8 k}{11}$ .

Given, there are $75$ more children than adults.

Thus, we have, $\frac{8 k}{11} - \frac{3 k}{11} = 75$

$\Rightarrow \frac{8 k - 3 k}{11} = 75$

$\Rightarrow \frac{5 k}{11} = 75$

$\Rightarrow k = 75 \div \frac{5}{11}$

$\Rightarrow k = 75 \times \frac{11}{5}$

$\Rightarrow k = \frac{75 \times 11}{5}$

$\Rightarrow k = \frac{5 \times 15 \times 11}{5}$

$\Rightarrow k = 165$

Now, $\frac{3 k}{11} = \frac{3 \times 165}{11} = \frac{3 \times 11 \times 15}{11} = 45$ and $165 - 45 = 120$ .

Therefore, there are $45$ adults and $120$ children in the restaurant.

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