Question

The ratio of adults to children in a movie theater is 7:2. If there are 26 children in the theater, how many adults are there?

Answer 1

Answer:

91 adults

Step-by-step explanation:

To find 5his anser you would decide 26 by to to find out how much each ratio is worth:

26÷2=13

thus tells us that each ratio is worth 13, so now we have to multiply 13 by 7 to find your final answer:

13×7=91

Answer 2

You can use the fact that ratio is a relative information of two measurement, which includes partial information about each of the measurement.

The number of adults in the theater specified for the given condition is 91

How to obtain real measurements from the ratio of two measurements?

Suppose the  real measurements were "a" and "b"

Then their ratio will be formed as

$\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}$

where $x$ is a common factor (not 1)

This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly cancelled from both the numerator and the denominator.

Thus, a = px, b = qx

How to get the number of adults in the movie theater?

Since the ratio of adults to children is 7:2, let the missing factor be x, then we have:

Number of adults = $7x$ (it is 7 times $x$, and usually, that multiplication sign is not written between constant and variable and is assumed to be present if there's no space)

Number of children = $2x$

Since there are 26 children, thus,

$2x = 26\\\text{dividing both the sides by 2}\\\\x = \dfrac{26}{2} = 13$(since 2x means 2 times x and dividing by 2 made that 2 with x turn to 1 times x : $\dfrac{2x}{2} = \dfrac{2 \times x}{2} = 1 \times x = x$)

Thus, number of adults = $7 \times x = 7 \times 13 = 91$

Thus,

The number of adults in the theater specified for the given condition is 91

Learn more about ratio and proportion here:

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