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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.
A. 30 years
B. 36 years
C. 45 years
D. 51 years

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

Full solution

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

Denote ages as variables: Let's denote the age of the man as $5x$ and the age of his wife as $4x$ , where $x$ is a common multiplier. $\newline$ The ratio of their ages is given as $5:4$ , which means for every $5$ units of age the man has, the wife has $4$ units of the same age.
Write sum equation: We know that the sum of their ages is $81$ years. So we can write the equation: $\newline$ $5x + 4x = 81$
Combine like terms: Combine like terms to solve for $x$ . $9x = 81$
Find value of x: Divide both sides of the equation by $9$ to find the value of x. $\newline$ $x = \frac{81}{9}$ $\newline$ $x = 9$
Calculate age of younger person: Now that we have the value of $x$ , we can find the age of the younger person, which is the wife with the age of $4x$ . $\newline$ Age of the younger person (wife) = $4 \times 9$
Calculate age of younger person: Now that we have the value of $x$ , we can find the age of the younger person, which is the wife with the age of $4x$ . $\newline$ Age of the younger person (wife) = $4 \times 9$ Calculate the age of the younger person. $\newline$ Age of the younger person = $36$ years

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