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The sum of the ages of a man and his wife is $81$ years. The ratio of their ages is $5:4$ . Find the age of the younger person. $\newline$ A. $30$ years $\newline$ B. $36$ years $\newline$ C. $45$ years $\newline$ D. $51$ years

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Write linear functions: word problems

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Q. The sum of the ages of a man and his wife is

81

years. The ratio of their ages is

5:4

. Find the age of the younger person.

\newline

A.

30

years

\newline

B.

36

years

\newline

C.

45

years

\newline

D.

51

years

Set up equations: Set up the equations based on the given information. $\newline$ Let the age of the man be $5x$ and the age of his wife be $4x$ , where $x$ is a common multiplier. According to the problem, the sum of their ages is $81$ years. $\newline$ So, the equation is $5x + 4x = 81$ .
Solve for x: Solve the equation for x. $\newline$ Combine like terms on the left side of the equation. $\newline$ $5x + 4x = 9x$ $\newline$ Now, divide both sides of the equation by $9$ to find $x$ . $\newline$ $9x = 81$ $\newline$ $x = \frac{81}{9}$ $\newline$ $x = 9$
Determine younger person's age: Determine the age of the younger person. $\newline$ Since the ratio of their ages is $5:4$ , and we are looking for the younger person, we will use the smaller multiplier, which is $4x$ . $\newline$ Age of the younger person = $4x = 4 \times 9 = 36$ years.

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